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Recent questions tagged ch9
Questions
The order and degree of the differential equation $\bigg(\frac{d^3y}{dx^3}\bigg)^2+3\frac{d^2y}{dx^2}+2\bigg(\frac{dy}{dx}\bigg)^4=y^4$ are
cbse
class12
ch9
q67
p200
objective
exemplar
sec-a
math
asked
Jan 20, 2013
by
sreemathi.v
1
answer
The solution of $\large\frac{dy}{dx}$$+y=e^{-x},y(0)=0$ is
cbse
class12
ch9
sec-a
q66
p200
objective
exemplar
medium
math
asked
Jan 20, 2013
by
sreemathi.v
1
answer
The differential equation for which $y=a\cos x+b\sin x$ is a solution is \[(A)\;\frac{d^2y}{dx^2}+y=0 \quad (B)\;\frac{d^2y}{dx^2}-y=0 \quad (C)\;\frac{d^2y}{dx^2}+(a+b)y=0 \quad (D)\;\frac{d^2y}{dx^2}+(a+b)y=0\]
cbse
class12
ch9
sec-a
q65
p200
objective
exemplar
easy
math
asked
Jan 20, 2013
by
sreemathi.v
1
answer
The solution of the equation $(2y-1)dx-(2x+3)dy=0$ is\[(A)\;\frac{2x-1}{2y+3}=k \quad (B)\;\frac{2y+1}{2x-3}=k \quad (C)\;\frac{2x+3}{2y-1}=k \quad (D)\;\frac{2x-1}{2y+1}=k \]
cbse
class12
ch9
sec-a
q64
p199
objective
exemplar
medium
math
asked
Jan 20, 2013
by
sreemathi.v
1
answer
The general solution of the differential equation $\large\frac{dy}{dx} $$=e^{\large\frac{x^2}{2}}+xy$ is :\[(A)\;y=ce^{\large\frac{x^2}{2}} \quad (B)\;y=-ce^{\large\frac{x^2}{2}} \quad (C)\;y=(x+c)e^{\large\frac{x^2}{2}} \quad (D)\;y=(c-x)e^{\large\frac{x^2}{2}}\]
cbse
class12
ch9
sec-a
q63
p199
objective
exemplar
medium
math
asked
Jan 19, 2013
by
sreemathi.v
1
answer
The curve for which the slope of the tangent at any point is equal to the ratio of the abscissa to the ordinate of the point is
class12
cbse
ch9
sec-a
q62
p199
objective
exemplar
easy
jeemain
differential-equations
math
asked
Jan 19, 2013
by
sreemathi.v
1
answer
The general solution of $\large\frac{dy}{dx}$$=2xe^{x^2-y}$ is: \[(A)\;e^{x^2-y}=c \quad (B)\;e^{-y}+e^{x^2}=c \quad(C)\;e^y=e^{x^2}+c \quad (D)\;e^{x^2}+y=c\]
cbse
class12
ch9
sec-a
q61
p199
objective
exemplar
easy
math
asked
Jan 19, 2013
by
sreemathi.v
1
answer
Family $Y=Ax+A^3$ of curves will correspond to a differential equation of order \[(A)\;3\quad(B)\;2\quad(C)\;1\;(D)\;not\;defined\]
cbse
class12
ch9
sec-a
q60
p199
objective
exemplar
easy
math
asked
Jan 19, 2013
by
sreemathi.v
1
answer
The differential equation of the family of curves $x^2+y^2-2ay=0$,where a is arbitrary constant,is\[(A)\;(x^2-y^2)\frac{dy}{dx}=2xy \quad (B)\;2(x^2+y^2)\frac{dy}{dx}=xy \quad (C)\;2(x^2-y^2)\frac{dy}{dx}=xy \quad (D)\;2(x^2+y^2)\frac{dy}{dx}=2xy\]
cbse
class12
ch9
sec-a
q59
p199
objective
exemplar
medium
math
asked
Jan 19, 2013
by
sreemathi.v
1
answer
The solution of $x \large\frac{dy}{dx}$$+y=e^x$ is:\[(A)\;y=\frac{e^x}{x}+\frac{k}{x} \quad (B)\;y=xe^x+cx \quad (C)\;y=xe^x+k \quad (D)\;x=\frac{e^y}{y}-\frac{k}{y}\]
cbse
class12
ch9
q58
p198
objective
exemplar
sec-a
math
asked
Jan 19, 2013
by
sreemathi.v
1
answer
The solution of the differential equation $\cos x\sin y\;dx+\sin x\cos y\;dy=0$ is:
cbse
class12
ch9
sec-a
q57
p198
objective
exemplar
medium
math
asked
Jan 19, 2013
by
sreemathi.v
1
answer
$y=ae^{mx}+be^{-mx}$ satisfies which of the following differential equation?
cbse
class12
ch9
sec-a
q56
p198
objective
exemplar
easy
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
The integrating factor of the differential equation $\Large \frac{dy}{dx}\normalsize+y=\Large \frac{1+y}{x}$ is
cbse
class12
ch9
sec-a
q55
p198
objective
exemplar
easy
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
The solution of the differential equation $\Large \frac{dy}{dx}=\frac{1-y^2}{1-x^2}$ is:\begin{array}{1 1}(A)\;y=\tan^{-1}x & (B)\;y-x=k(1+xy)\\(C)\;x=tan^{-1}y & (D)\;\tan (xy)=k\end{array}
cbse
class12
ch9
sec-a
q54
p198
objective
exemplar
difficult
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Integrating factor of the differential equation $\large\frac{dy}{dx}$$+y\tan x-\sec x=0$ is \begin{array}{1 1}(A)\;\cos x & (B)\;sec x\\(C)\;e^{\cos x} & (D)\;e^{\sec x} \end{array}
cbse
class12
ch9
sec-a
q53
p198
objective
exemplar
easy
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
The solution of $\Large \frac{dy}{dx}\normalsize +y=e^{-x},y(0)=0$ is:\begin{array}{1 1}(A)\;y=e^x(x-1) & (B)\;y=xe^{-x}\\(C)\;y=xe^{-x}+1 & (D)\;y=(x+1)e^{-x}\end{array}
cbse
class12
ch9
sec-a
q52
p197
objective
exemplar
medium
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
The degree of the differential equation $\large\frac{d^2y}{dx^2}+\bigg(\frac{dy}{dx}\bigg)^3$$+6y^5=0$ is\[(A)\;1\quad(B)\;2\quad(C)\;3\quad(D)\;5\]
cbse
class12
ch9
sec-a
q51
p197
objective
exemplar
easy
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
The general solution of $e^x\cos y\;dx-e^x\sin y\;dy=0$ is:\begin{array}{1 1}(A)\;e^x\cos y=c & (B)\;e^x\sin y=c\\(C)\;e^x=c\;\cos y & (D)\;e^x=c\;\sin y\end{array}
cbse
class12
ch9
sec-a
q50
p197
objective
exemplar
easy
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
The differential equation $y\Large \frac{dy}{dx}\normalsize+x=c$ represents:\begin{array}{1 1}(A)\;family \;of \;hyperbolas & (B)\;family \;of \;parabolas \\(C)\;family \;of \;ellipses & (D)\;family\; of \;circles\end{array}
cbse
class12
ch9
sec-a
q49
p197
objective
exemplar
medium
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
$\tan^{-1}x+\tan^{-1}y=c$ is the general solution of the differential equation:
cbse
class12
ch9
sec-a
q48
p197
objective
exemplar
easy
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Integrating factor of the differential equation $(1-x^2)\Large \frac{dy}{dx}\normalsize -xy=1$ is \[(A)\;-x\quad(B)\;\frac{x}{1-x^2}\quad(C)\;\sqrt {1-x^2}\quad(D)\;\frac{1}{2}log(1-x^2)\]
cbse
class12
ch9
sec-a
q47
p197
objective
exemplar
difficult
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Which of the following is a second order differential equation\begin{array}{1 1}(A)\;(y')^2+x=y^2 & (B)\;y' y''+y=\sin x\\(C)\;y'''+(y'')^2+y=0 & (D)\;y'=y^2\end{array}
cbse
class12
ch9
sec-a
q46
p197
objective
exemplar
easy
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
The number of solutions of$\Large\frac{dy}{dx}=\Large\frac{y+1}{x-1}$ when y(1)=2 is\[(A)\;none\quad(B)\;one\quad(C)\;two\quad(D)\;infinite\]
cbse
class12
ch9
q45
p197
objective
exemplar
sec-a
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Solution of $\Large \frac{dy}{dx}$$-y=1,y(0)=1$ is given by \[(A)\;xy=-e^x\quad(B)\;xy=-e^{-x}\quad(C)\;xy=-1\quad(D)\;y=2e^x-1\]
cbse
class12
ch9
sec-a
q44
p196
objective
exemplar
medium
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Integrating factor of $x\Large \frac{dx}{dy}\normalsize-y=x^4-3x$ is \[(A)\;x\quad(B)\;log x\quad(C)\;\frac{1}{x}\quad(D)\;-x\]
cbse
class12
ch9
sec-a
q43
p196
objective
exemplar
easy
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Family $y=Ax+A^3$ of curves is represented by the differential equation of degree\[(A)\;1\quad(B)\;2\quad(C)\;3\quad(D)\;4\]
cbse
class12
ch9
sec-a
q42
p196
objective
exemplar
easy
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Solution of the differential equation $\tan y\sec^2x dx+\tan x\sec^2y dy=0$ is \[(A)\;\tan x+\tan y=c \quad (B)\;\tan x-\tan y=c \quad(C)\;\frac{\tan x}{\tan y}=c \quad (D\;\tan x.tan y=c\]
cbse
class12
ch9
sec-a
q41
p196
objective
exemplar
medium
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Integrating factor of the differential equation $\cos x\large\frac{dy}{dx}$$+y\sin x=1$ is:\[(A)\;\cos x\quad(B)\;\tan x\quad(C)\;\sec x\quad(D)\;\sin x\]
cbse
class12
ch9
sec-a
q40
p196
objective
exemplar
medium
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Solution of differential equation $x dy-y dx=0$ represents:
cbse
class12
ch9
sec-a
q39
p196
objective
exemplar
easy
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
The differential equation for $y=A\cos\alpha x+B\sin\alpha x,$where A and B are arbitrary constants is\begin{array}{1 1}(A)\;\frac{d^2y}{dx^2}+x^2y=0 & (B)\;\frac{d^2y}{dx^2}+\alpha^2y=0\\(C)\;\frac{d^2y}{dx^2}+y=0 & (D)\;\frac{d^2y}{dx^2}-y=0\end{array}
cbse
class12
ch9
sec-a
q38
p196
objective
exemplar
easy
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
If $y=e^{-x}(A\cos x+B\sin x)$, then $y$ is a solution of
cbse
class12
ch9
differential-equations
sec-a
q37
p195
objective
exemplar
difficult
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
The order and degree of the differential equation $\large\frac{d^2y}{dx^2}+\bigg(\frac{dy}{dx}\bigg)^{\frac{1}{4}}+x^{\frac{1}{5}}=0$,respectively,are\[(A)\;2\;and\;not\;defined\quad(B)\;2\;and\;2\quad(C)\;2\;and\;3\quad(D)\;3\;and\;3\]
cbse
class12
ch9
sec-a
q36
p195
objective
exemplar
easy
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
The degree of the differential equation $1+\bigg[\bigg(\large\frac{dy}{dx}\bigg)^2\bigg]^{\large\frac{3}{2}}=\frac{d^2y}{dx^2}$ is:\[(A)\;4\quad(B)\;\frac{3}{2}\quad(C)\;not\;defined\quad(D)\;2\]
cbse
class12
ch9
sec-a
q35
p195
objective
exemplar
easy
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
The degree of the differential equation $\large\bigg(\frac{d^2y}{dx^2}\bigg)^2+\bigg(\frac{dy}{dx}\bigg)^2$$=x\sin \bigg(\large\frac{dy}{dx}\bigg)$ is:\[(A)\;1\quad(B)\;2\quad(C)\;3\quad(D)\;not\;defined\]
cbse
class12
ch9
sec-a
q34
p195
objective
exemplar
easy
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Solve: $x\large \frac{dy}{dx}$$ =y(\log y-\log x+1)$
cbse
class12
ch9
sec-a
q33
p195
exemplar
medium
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Find the equation of a curve passing through the point (1,1).If the tangent drawn at any point P(x,y) on the curve meets the coordinate axes at A and B such that P is the mid-point of AB.
cbse
class12
ch9
sec-b
q32
p195
exemplar
difficult
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Find the equation of a curve passing through origin if the slope of the tangent to the curve at any point $(x,y)$ is equal to the square of the difference of the abscissa and the ordinate of the point.
cbse
class12
ch9
sec-b
q31
p195
exemplar
medium
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Find the equation of the curve through the point (1,0) if the slope of the tangent to the curve at any point (x,y) is $\Large \frac{y-1}{x^2+x}.$
cbse
class12
ch9
sec-b
q30
p195
exemplar
medium
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Find the equation of a curve passing through (2,1) if the slope of the tangent to the curve at any point (x,y) is $\Large \frac{x^2+y^2}{2xy}.$
cbse
class12
ch9
sec-b
q29
p194
exemplar
difficult
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Find the general solution of $\large \frac{dy}{dx}$$+3y=\sin 2x$
cbse
class12
ch9
sec-b
q28
p194
exemplar
difficult
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Solve :$\large\frac{dy}{dx}$$=\cos (x+y)+\sin (x+y)$.[Hint :Substitute x+y=z]
cbse
class12
ch9
sec-b
q27
p194
exemplar
difficult
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
FInd the general solution of $(1+\tan y)(dx-dy)+2xdy=0$
cbse
class12
ch9
sec-a
q26
p194
exemplar
difficult
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Solve:$y+\large\frac{d}{dx}$$(xy)=x(\sin x+log x)$
cbse
class12
ch9
sec-b
q25
p194
exemplar
difficult
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Find the differential equation of system of concentric circles with centre(1,2).
cbse
class12
ch9
sec-a
q24
p194
short-answer
exemplar
easy
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Solve the differential equation $(1+y^2)\tan^{-1}xdx+2y(1+x^2)dy=0$
cbse
class12
ch9
sec-b
q23
p194
short-answer
exemplar
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Form the differential equation by eliminating A and B in $Ax^2+By^2=1$.
cbse
class12
ch9
sec-b
q22
p194
short-answer
exemplar
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Solve the differential equation $dy=\cos x(2-y\; cosec x)dx$ given that $y=2$ when $x=\Large\frac{\pi}{2}$.
cbse
class12
ch9
sec-b
q21
p194
short-answer
exemplar
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Solve: $2(y+3)-xy\Large\frac{dy}{dx}\normalsize =0,$given that $y(1)=-2$
cbse
class12
ch9
sec-b
q20
p194
short-answer
exemplar
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Solve: $(x+y)(dx-dy)=dx+dy.$[Hint:Substitute x+y=z after separating dx and dy]
cbse
class12
ch9
sec-b
q19
p194
short-answer
exemplar
difficult
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Find the general solution of $y^2dx+(x^2-xy+y^2)dy=0$
cbse
class12
ch9
sec-b
q18
p194
short-answer
exemplar
difficult
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
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