Recent questions in Differential Equations

True-or-False: The solution of the differential equation $\large\frac{dy}{dx} = \frac{x+2y}{x}$ is $x+y=kx^2$.

asked Jan 21, 2013 by sreemathi.v

1 answer

True-or-False: Differential equation representing the family of curves $y=e^x(A\cos x+B\sin x)$ is $\frac{d^2y}{dx^2} - 2\frac{dy}{dx} + 2y = 0$.

asked Jan 21, 2013 by sreemathi.v

1 answer

True-or-False: The solution of $\large\frac{dy}{dx}$$=\bigg(\large\frac{y}{x}\bigg)^\frac{1}{3}$ is $y^{\large\frac{2}{3}}-x^{\large\frac{2}{3}}=c$.

asked Jan 20, 2013 by sreemathi.v

1 answer

True-or-False: The differential equation representing the family of circles $x^2+(y-a)^2=a^2$ will be of order two.

asked Jan 20, 2013 by sreemathi.v

1 answer

True-or-False: Number of arbitrary constant in the particular solution of a differential equation of order two is two.

asked Jan 20, 2013 by sreemathi.v

1 answer

True-or-False: Correct substitution for the solution of the differential equation of the type $\large\frac{dx}{dy}$$=g(x,y)$,where $g(x,y)$ is a homogeneous function of zero degree is $x=vy.$

asked Jan 20, 2013 by sreemathi.v

1 answer

True-or-False: Correct substitution for the solution of the differential equation of the type $\large\frac{dy}{dx}$$=f(x,y)$,where f(x,y) is a homogeneous function of zero degree is $y=vx.$

asked Jan 20, 2013 by sreemathi.v

1 answer

True-or-False: Solution of the differential equation of the type $\large\frac{dx}{dy}$$+P_1x=Q_1$ is given by $x.(I.F)=\int (I.F)Q_1dy.$

asked Jan 20, 2013 by sreemathi.v

1 answer

True-or-False: Integrating factor of the differential equation of the form $\large\frac{dx}{dy}$$+P_1x=Q_1$ is given by $e^{\int P_1dy}$.

asked Jan 20, 2013 by sreemathi.v

1 answer

The integrating factor of $\large\frac{dy}{dx}-y=\frac{1-y}{x}$ is__________.

asked Jan 20, 2013 by sreemathi.v

1 answer

The solution of the differential equation $\cot y dx=xdy$ is __________.

asked Jan 20, 2013 by sreemathi.v

1 answer

The general solution of $\frac{dy}{dx}-y=\sin x$ is

asked Jan 20, 2013 by sreemathi.v

1 answer

The solution of the differential equation $y dx + (x + xy) dy = 0$ is

asked Jan 20, 2013 by sreemathi.v

1 answer

The solution of $(1+x^2)\frac{dy}{dx}+2xy-4x^2=0$ is ___________.

asked Jan 20, 2013 by sreemathi.v

1 answer

The solution of the differential equation $x\large\frac{dy}{dx}$$+2y=x^2$ is

asked Jan 20, 2013 by sreemathi.v

1 answer

General solution of the differential equation of the type $\Large\frac{dy}{dx}$$+P_1x=Q_1$ is given by ______.

asked Jan 20, 2013 by sreemathi.v

1 answer

$\large\frac{dy}{dx}+\frac{y}{xlog x}=\frac{1}{x}$ is an equation of the type _____________.

asked Jan 20, 2013 by sreemathi.v

1 answer

The number of arbitrary constants in the general solution of a differential equation of order three is ________.

asked Jan 20, 2013 by sreemathi.v

1 answer

The degree of the differential equation $\sqrt{1+\bigg(\large\frac{dy}{dx}\bigg)^2}$$=x$ is ___________.

asked Jan 20, 2013 by sreemathi.v

1 answer

The degree of the differential equation $\large\frac{d^2y}{dx^2}$$+e^{\large\frac{dy}{dx}}$$=0$ is __________.

asked Jan 20, 2013 by sreemathi.v

1 answer

The solution of the differential equation $\large\frac{dy}{dx}+\frac{2xy}{(1+x^2)}=\frac{1}{(1+x^2)^2}$ is

asked Jan 20, 2013 by sreemathi.v

1 answer

The solution of the differential equation $\large\frac{dy}{dx}$$=e^{x-y}+x^2e^{-y}$ is

asked Jan 20, 2013 by sreemathi.v

1 answer

The general solution of the differential equation $(e^x+1)ydy=(y+1)e^xdx$ is

asked Jan 20, 2013 by sreemathi.v

1 answer

Solution of the differential equation $\large\frac{dy}{dx}+\frac{y}{x}$$=\sin x$ is:

asked Jan 20, 2013 by sreemathi.v

1 answer

General solution of $\frac{dy}{dx} + y\tan x = \sec x$ is

asked Jan 20, 2013 by sreemathi.v

1 answer

Which of the following is the general solution of $\large\frac{d^2y}{dx^2}$$-2\large\frac{dy}{dx}$$+y=0$

asked Jan 20, 2013 by sreemathi.v

1 answer

The differential equation of the family of curves $y^2=4a(x+a)$ is

asked Jan 20, 2013 by sreemathi.v

1 answer

The order and degree of the differential equation $\bigg[1+\bigg(\large\frac{dy}{dx}\bigg)^2\bigg]=\bigg(\large\frac{d^2y}{dx^2}\bigg)$ are

asked Jan 20, 2013 by sreemathi.v

1 answer

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

asked Jan 20, 2013 by sreemathi.v

1 answer

The solution of $\large\frac{dy}{dx}$$+y=e^{-x},y(0)=0$ is

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 \[(A)\;\frac{d^2y}{dx^2}+y=0 \quad (B)\;\frac{d^2y}{dx^2}-y=0 \quad (C)\;\frac{d^2y}{dx^2}+(a+b)y=0 \quad (D)\;\frac{d^2y}{dx^2}+(a+b)y=0\]

asked Jan 20, 2013 by sreemathi.v

1 answer

The solution of the equation $(2y-1)dx-(2x+3)dy=0$ is\[(A)\;\frac{2x-1}{2y+3}=k \quad (B)\;\frac{2y+1}{2x-3}=k \quad (C)\;\frac{2x+3}{2y-1}=k \quad (D)\;\frac{2x-1}{2y+1}=k \]

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 :\[(A)\;y=ce^{\large\frac{x^2}{2}} \quad (B)\;y=-ce^{\large\frac{x^2}{2}} \quad (C)\;y=(x+c)e^{\large\frac{x^2}{2}} \quad (D)\;y=(c-x)e^{\large\frac{x^2}{2}}\]

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

asked Jan 19, 2013 by sreemathi.v

1 answer

The general solution of $\large\frac{dy}{dx}$$=2xe^{x^2-y}$ is: \[(A)\;e^{x^2-y}=c \quad (B)\;e^{-y}+e^{x^2}=c \quad(C)\;e^y=e^{x^2}+c \quad (D)\;e^{x^2}+y=c\]

asked Jan 19, 2013 by sreemathi.v

1 answer

Family $Y=Ax+A^3$ of curves will correspond to a differential equation of order \[(A)\;3\quad(B)\;2\quad(C)\;1\;(D)\;not\;defined\]

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\[(A)\;(x^2-y^2)\frac{dy}{dx}=2xy \quad (B)\;2(x^2+y^2)\frac{dy}{dx}=xy \quad (C)\;2(x^2-y^2)\frac{dy}{dx}=xy \quad (D)\;2(x^2+y^2)\frac{dy}{dx}=2xy\]

asked Jan 19, 2013 by sreemathi.v

1 answer

The solution of $x \large\frac{dy}{dx}$$+y=e^x$ is:\[(A)\;y=\frac{e^x}{x}+\frac{k}{x} \quad (B)\;y=xe^x+cx \quad (C)\;y=xe^x+k \quad (D)\;x=\frac{e^y}{y}-\frac{k}{y}\]

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:

asked Jan 19, 2013 by sreemathi.v

1 answer

$y=ae^{mx}+be^{-mx}$ satisfies which of the following differential equation?

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

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}

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}

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}

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\[(A)\;1\quad(B)\;2\quad(C)\;3\quad(D)\;5\]

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}

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}

asked Jan 18, 2013 by sreemathi.v

1 answer

$\tan^{-1}x+\tan^{-1}y=c$ is the general solution of the differential equation:

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 \[(A)\;-x\quad(B)\;\frac{x}{1-x^2}\quad(C)\;\sqrt {1-x^2}\quad(D)\;\frac{1}{2}log(1-x^2)\]

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}

asked Jan 18, 2013 by sreemathi.v

1 answer

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