Recent questions tagged exemplar

Solution of the differential equation $\tan y\sec^2x dx+\tan x\sec^2y dy=0$ is \[(A)\;\tan x+\tan y=c \quad (B)\;\tan x-\tan y=c \quad(C)\;\frac{\tan x}{\tan y}=c \quad (D\;\tan x.tan y=c\]

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:\[(A)\;\cos x\quad(B)\;\tan x\quad(C)\;\sec x\quad(D)\;\sin x\]

asked Jan 18, 2013 by sreemathi.v

1 answer

Solution of differential equation $x dy-y dx=0$ represents:

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}

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

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\[(A)\;2\;and\;not\;defined\quad(B)\;2\;and\;2\quad(C)\;2\;and\;3\quad(D)\;3\;and\;3\]

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:\[(A)\;4\quad(B)\;\frac{3}{2}\quad(C)\;not\;defined\quad(D)\;2\]

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:\[(A)\;1\quad(B)\;2\quad(C)\;3\quad(D)\;not\;defined\]

asked Jan 18, 2013 by sreemathi.v

1 answer

Solve: $x\large \frac{dy}{dx}$$ =y(\log y-\log x+1)$

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.

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.

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 $\Large \frac{y-1}{x^2+x}.$

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 $\Large \frac{x^2+y^2}{2xy}.$

asked Jan 18, 2013 by sreemathi.v

1 answer

Find the general solution of $\large \frac{dy}{dx}$$+3y=\sin 2x$

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]

asked Jan 18, 2013 by sreemathi.v

1 answer

FInd the general solution of $(1+\tan y)(dx-dy)+2xdy=0$

asked Jan 18, 2013 by sreemathi.v

1 answer

Solve:$y+\large\frac{d}{dx}$$(xy)=x(\sin x+log x)$

asked Jan 18, 2013 by sreemathi.v

1 answer

Find the differential equation of system of concentric circles with centre(1,2).

asked Jan 18, 2013 by sreemathi.v

1 answer

Solve the differential equation $(1+y^2)\tan^{-1}xdx+2y(1+x^2)dy=0$

asked Jan 18, 2013 by sreemathi.v

1 answer

Form the differential equation by eliminating A and B in $Ax^2+By^2=1$.

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 $x=\Large\frac{\pi}{2}$.

asked Jan 18, 2013 by sreemathi.v

1 answer

Solve: $2(y+3)-xy\Large\frac{dy}{dx}\normalsize =0,$given that $y(1)=-2$

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]

asked Jan 18, 2013 by sreemathi.v

1 answer

Find the general solution of $y^2dx+(x^2-xy+y^2)dy=0$

asked Jan 18, 2013 by sreemathi.v

1 answer

Find the general solution of the differential equation $(1+y^2)+(x-e^{\large\tan^{-1}y})\Large \frac{dy}{dx}$=0

asked Jan 18, 2013 by sreemathi.v

1 answer

Solve: $x^2\Large \frac{dy}{dx}\normalsize =x^2+xy+y^2$

asked Jan 18, 2013 by sreemathi.v

1 answer

Find the equation of a curve passing through origin and satisfying the differential equation $(1-x^2)\Large \frac{dy}{dx}\normalsize-2xy=4x^2$

asked Jan 18, 2013 by sreemathi.v

1 answer

Form the differential equation of all circles which pass through origin and whose centers lie on y-axis as shown below:

asked Jan 18, 2013 by sreemathi.v

1 answer

Form the differential equation having $y=(\sin^{-1}x)^2+A\cos^{-1}x+B,$where A and B are arbitrary constants,as its general solution.

asked Jan 18, 2013 by sreemathi.v

1 answer

If y(t) is a solution of $(1+t)\Large\frac{dy}{dt}\normalsize-ty=1$ and $y(0)=-1,$ then show that y(1)=$-\Large \frac{1}{2}$

asked Jan 18, 2013 by sreemathi.v

1 answer

If y(x) is a solution of $\Large\frac{2-\sin x}{1-y}\bigg(\frac{dy}{dx}\bigg)\normalsize=-\cos x$ and y(0)=1,then find the value of $\frac{1}{2}.$

asked Jan 18, 2013 by sreemathi.v

1 answer

Find the general solution of $(x+2y^3)\Large \frac{dy}{dx}\normalsize =y \;dx$

asked Jan 17, 2013 by sreemathi.v

1 answer

Solve the differential equation $\Large \frac{dy}{dx}\normalsize=1+x+y^2+xy^2,$when y=0,x=0.

asked Jan 17, 2013 by sreemathi.v

1 answer

Solve:$y\;dx-x\;dy=x^2y\;dx$

asked Jan 17, 2013 by sreemathi.v

1 answer

Solve the differential equation $\Large\frac{dy}{dx}\normalsize+1=e^{x+y}$

asked Jan 17, 2013 by sreemathi.v

1 answer

Find the general solution of $\Large \frac{dy}{dx}\normalsize =ay-e^{mx}$

asked Jan 17, 2013 by sreemathi.v

1 answer

Solve the differential equation$\Large \frac{dy}{dx}\normalsize =2xy-y$

asked Jan 17, 2013 by sreemathi.v

1 answer

Solve the differential equation $(x^2-1)\Large \frac{dy}{dx}\normalsize +2xy=\Large \frac{1}{x^2-1}$

asked Jan 17, 2013 by sreemathi.v

1 answer

Given that $\large \frac{dy}{dx} = e^{-2y}$ and $y=0$ when $x=5$. Find the value of $x$ when $y=3$.

asked Jan 17, 2013 by sreemathi.v

1 answer

Find the differential equation of all non vertical lines in a plane.

asked Jan 17, 2013 by sreemathi.v

1 answer

Find the solution of $\Large \frac{dy}{dx}\normalsize =2^{y-x}.$

asked Jan 17, 2013 by sreemathi.v

1 answer

True-or-false: If $\overrightarrow{a}$ and $\overrightarrow{b}$ are adjacent sides of a rhombus,then $\overrightarrow{a}.\overrightarrow{b}=0$

asked Jan 17, 2013 by sreemathi.v

1 answer

True-or-False: The formula $(\overrightarrow{a}+\overrightarrow{b})^2=\mid{\overrightarrow{a}\mid}^2+\mid{\overrightarrow{b}\mid}^2\;+2\mid\overrightarrow{a}\mid.\mid\overrightarrow{b}\mid$ is valid for non-zero vectors $\overrightarrow{a}$ and $\overrightarrow{b}.$

asked Jan 17, 2013 by sreemathi.v

1 answer

True-or-False: If $\mid \overrightarrow{a}+\overrightarrow{b}\mid=\mid \overrightarrow{a}-\overrightarrow{b}\mid$,then the vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ are orthogonal.

asked Jan 17, 2013 by sreemathi.v

1 answer

True-or-False: Position vector of a point P is a vector whose initial point is origin.

asked Jan 17, 2013 by sreemathi.v

1 answer

True-or-False: If $\mid\overrightarrow{ a}\mid=\mid\overrightarrow {b}\mid$,then necessarily it implies $\overrightarrow{ a}=\overrightarrow {b}.$

asked Jan 17, 2013 by sreemathi.v

1 answer

If $\overrightarrow a$ is any non-zero vector ,then $(\overrightarrow a.\hat i)\hat i\;+(\overrightarrow a.\hat j)\hat j\;+(\overrightarrow a.\hat k)\hat k$ equals__________.

asked Jan 17, 2013 by sreemathi.v

1 answer

If ${\mid\overrightarrow{a}\times\overrightarrow{b}\mid}^2$=${\mid\overrightarrow{a}.\overrightarrow{b}\mid}^2=144$ and$\mid\overrightarrow{a}\mid=4,$ then $\mid\overrightarrow{b}\mid$ is equal to ________.

asked Jan 17, 2013 by sreemathi.v

1 answer

The value of the expression ${\mid \overrightarrow{a}\times \overrightarrow{b}\mid}^2+(\overrightarrow{a}.\overrightarrow{b})^2$ is _________.

asked Jan 17, 2013 by sreemathi.v

1 answer

The values of k for which $\mid k\overrightarrow{a}\mid\le\mid\overrightarrow{a}\mid$ and $k\overrightarrow{a}+\frac{1}{2}\overrightarrow{a}$ is parallel to $\overrightarrow{a}$ holds true are_________.

asked Jan 17, 2013 by sreemathi.v

1 answer

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