Recent questions in Differential Equations

Show that the differential equation is homogeneous and solve $\left\{x\cos\bigg(\large\frac{y}{x}\bigg)\normalsize+y\sin\bigg(\large\frac{y}{x}\bigg)\right\}ydx=\left\{y\sin\bigg(\large\frac{y}{x}\bigg)-\normalsize x\cos\bigg(\large\frac{y}{x}\bigg)\right\}\normalsize xdy$

asked Nov 29, 2012 by sreemathi.v

1 answer

Show that the differential equation is homogeneous and solve $x\large\frac{dy}{dx}$$-y+x\sin\bigg(\large\frac{y}{x}\bigg)=$$0$

asked Nov 29, 2012 by sreemathi.v

1 answer

Show that the differential equation is homogeneous and solve $y\: dx+x\log\bigg(\large\frac{y}{x}\bigg)$$dy-2x\;dy=0$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the particular solution satisfying the given condition $(x+y)dy+(x-y)dx=0;\;y=1;\;when\;x=\;1$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the particular solution satisfying the given condition $x^2dy+(xy+y^2)\;dx=0;y=\;1;\;when\;x=\;1$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the particular solution satisfying the given condition $\large\frac{dy}{dx}-\large\frac{y}{x}$$+cosec\bigg(\large\frac{y}{x}\bigg)$$=0;\;y=\;0\;when\;x=\;1$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the particular solution satisfying the given condition $2xy+y^2-2x^2\large\frac{dy}{dx}$$=0;\;y=\;2\;when\;x=\;1$

asked Nov 29, 2012 by sreemathi.v

1 answer

A homogeneous differential equation of the form $\frac{\large dx}{\large dy}=h\bigg(\frac{\large x}{\large y}\bigg)$ can be solved by making the substitution

asked Nov 29, 2012 by sreemathi.v

1 answer

Which of the following is a homogeneous differential equation?

asked Nov 29, 2012 by sreemathi.v

1 answer

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

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation$\large\frac{dy}{dx}$$+3y=e^{-2x}$

asked Nov 29, 2012 by sreemathi.v

1 answer

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

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation$\large\frac{dy}{dx}$$+(\sec x)y=\tan x\bigg(0\leq x<\large\frac{\pi}{2}\bigg)$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation $\cos^2x\large\frac{dy}{dx}$$+y=\tan x\bigg(0\leq x<\large\frac{\pi}{2}\bigg)$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation $x\large\frac{dy}{dx}$$+2y=x^2\log x$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation $x \log x\large\frac{dy}{dx}$$+y=\large\frac{2}{x}$$\log x$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation $(1+x^2)dy+2xy\;dx=\cot x\;dx\;(x\neq0)$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation $x\large\frac{dy}{dx}$$+y-x+xy\cot x=0\;(x\neq0)$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation $(x+y)\large\frac{dy}{dx}$$=1$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation $y\;dx+(x-y^2)dy=0$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation $(x+3y^2)\large\frac{dy}{dx}=y$$\;(y>0)$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find a particular solution satisfying the given condition$\large\frac{dy}{dx}$$+2y\tan x=\sin x;\;y=o\;when\;x=\large\frac{\pi}{3}$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find a particular solution satisfying the given condition $(1+x^2)\large\frac{dy}{dx}$$+2xy=\large\frac{1}{1+x^2}$$;y=0\;when\;x=1$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find a particular solution satisfying the given condition $\large\frac{dy}{dx}-$$3y\cot x=\sin 2x;\;y=2\;when\;x=\large\frac{\pi}{2}$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the equation of curve passing through the origin given that the slope of the tangent to the curve at any point $(x,y)$ is equal to the sum of the coordinates of the point .

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the equation of curve passing through the point(0,2) given that the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangent to the curve at that point by 5

asked Nov 29, 2012 by sreemathi.v

1 answer

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

asked Nov 29, 2012 by sreemathi.v

1 answer

The integrating factor of the differential equation $(1-y^2)\large\frac{dx}{dy}$$+yx=ay\: \;is$

asked Nov 29, 2012 by sreemathi.v

1 answer

verify that the given function (implicit or explicit) is a solution of the corresponding differential equation

asked Nov 29, 2012 by sreemathi.v

1 answer

Form the differential equation representing the family of curves given by $(x-a)^2+2y^2\;=\;a^2$, where $a$ is an arbitrary constant

asked Nov 29, 2012 by sreemathi.v

1 answer

Prove that $x^2-y^2\;=\;c(x^2+y^2)^2$is the general solution of differential equation $(x^3-3x\;y^2)dx\;=\;(y^3-3x^2y)dy$ where $c$ is a parameter.

asked Nov 29, 2012 by sreemathi.v

1 answer

Form the differential equation of the family of circles in the first quadrant which touch the coordinate axes.

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation$\large\frac{dy}{dx}+\sqrt{\frac{1-y^2}{1-x^2}}\;$$=\;0$

asked Nov 29, 2012 by sreemathi.v

1 answer

Show that the general solution of the differential equation$\large\frac{dy}{dx}+\large\frac{y^2+y+1}{x^2+x+1}=0$ is given by $(x+y+1)\;=\;A(1-x-y-2xy)$, where A is parameter

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the equation of the curve passing through the point$\bigg(0,\large\frac{\pi}{4}\bigg)$ whose differential equation is $\sin x\cos y\;dx+\cos x\sin y\;dy\;=\;0$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the particular solution of the differential equation $(1+e^{2x})dy + (1+y^2)e^xdx$ = 0, given that $y = 1$ when $x = 0$

asked Nov 29, 2012 by sreemathi.v

1 answer

Solve the differential equation$y\;e^{\large\frac{x}{y}}\;dx=\bigg(x\;e^{\Large\frac{x}{y}}+y^2\bigg)dy\;(y\neq0)$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find a particular solution of the differential equation $(x-y)(dx+dy) = dx - dy$,given that $ y=\;-1$,when $ x=\;0$

asked Nov 29, 2012 by sreemathi.v

1 answer

Solve the differential equation $\begin{bmatrix}\large\frac{e^{-2\sqrt{x}}}{\sqrt{x}}-\large\frac{y}{\sqrt{x}}\end{bmatrix}\large\frac{dx}{dy}$$=1(x\neq0)$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find a particular solution of the differential equation $\frac{dy}{dx} + y\cot x=4x\:cosec\:x$, $(x\neq0)$, given that $y = 0$ when $x = \large\frac{\pi}{2}$

asked Nov 28, 2012 by sreemathi.v

1 answer

Find a particular solution of the differential equation $(x+1)\frac{dy}{dx}=2e^{-y} -1$, given that $y = 0$ when $x = 0$.

asked Nov 28, 2012 by sreemathi.v

1 answer

The population of a village increases continuously at the rate proportional to the number of its inhabitants present at any time.If the population was 20,000 in 1999 and 25000 in the year of 2004,what will be the population of the village in 2009?

asked Nov 28, 2012 by sreemathi.v

1 answer

The general solution of the differential equation $\large\frac{ydx-xdy}{y}$$=0\;is$

asked Nov 28, 2012 by sreemathi.v

1 answer

The general solution of a differential equation of the type $\large\frac{dx}{dy}$$+p_1x=Q_1\;is$

asked Nov 28, 2012 by sreemathi.v

1 answer

The general solution of the differential equation$ e^xdy+(ye^x+2x)dx=0\; is$

asked Nov 28, 2012 by sreemathi.v

1 answer

For each of the differential equations given below,indicate its order and degree(if defined) $(i)\;\large\frac{d^2y}{dx^2}+5x\bigg(\frac{dy}{dx}\bigg)^2-6y=\log x$

asked Nov 28, 2012 by sreemathi.v

1 answer

The order of the differential equation $2x^2\large\frac{d^2y}{dx^2}$$-3\frac{dy}{dx}$$+y=0\;is$

asked Nov 28, 2012 by sreemathi.v

1 answer

The degree of the differential equation $\bigg(\large\frac{d^2y}{dx^2}\bigg)^3+\bigg(\frac{dy}{dx}\bigg)^2$$+\sin\bigg(\large\frac{dy}{dx}\bigg)$$+1=0\; is$

asked Nov 28, 2012 by sreemathi.v

1 answer

Determine order and degree (if defined) of differential equation $y''+2y'+\sin y=0$

asked Nov 28, 2012 by sreemathi.v

1 answer

Determine order and degree (if defined) of differential equation $y''+(y')^2+2y=0$

asked Nov 28, 2012 by sreemathi.v

1 answer

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