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Recent questions tagged ch9

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

For the differential equations, find the particular solution satisfying the given condition: \[ \bigg[ x \: sin^2 \bigg( \frac{x}{y} - y \bigg) \bigg] dx + xdy = 0; y \frac{\large \pi}{\large 4} when \: x = 1\]

asked Dec 12, 2012 by thanvigandhi_1

1 answer

Show that the differential equation is homogeneous and solve :$ \bigg( 1 + e^{\Large\frac{x}{y}} \bigg) dx + e^{\Large\frac{x}{y}} \bigg( 1 -\large \frac{x}{y} \bigg) $$dy= 0 $

asked Dec 12, 2012 by thanvigandhi_1

1 answer

Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation $y=e^x+1\qquad:\;y''-y'=0$

asked Nov 30, 2012 by sreemathi.v

1 answer

Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation $y=x^2+2x+C\qquad:\;y'-2x-2=0$

asked Nov 30, 2012 by sreemathi.v

1 answer

Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation $y=\cos x+C\qquad:y'+\sin x=0$

asked Nov 30, 2012 by sreemathi.v

1 answer

Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation\[y=\sqrt{1+x^2}\qquad:\;y'\;=\frac{xy}{1+x^2}\]

asked Nov 30, 2012 by sreemathi.v

1 answer

Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation $y=Ax\qquad:\;xy'\;=\;y\;(x\neq0)$

asked Nov 30, 2012 by sreemathi.v

1 answer

Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation $y=x\sin x\qquad:xy'=y+x\sqrt{x^2-y^2} (x\neq0\;and\;x>y\;or\;x<-y)$

asked Nov 30, 2012 by sreemathi.v

1 answer

Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation $xy=\log\: y+C\qquad:y'=\large\frac{y^2}{1-xy}$$\;(xy\neq1)$

asked Nov 30, 2012 by sreemathi.v

1 answer

Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation $y-\cos y=x\qquad:\;(y\sin y+\cos y+x)y'=y$

asked Nov 30, 2012 by sreemathi.v

1 answer

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

asked Nov 30, 2012 by sreemathi.v

1 answer

Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation $y=\sqrt{a^2-x^2}\;x\in\;(-a,a):\;x+y\;\large\frac{dy}{dx}$$=0(y\neq0)$

asked Nov 30, 2012 by sreemathi.v

1 answer

The number of arbitrary constants in the general solution of a differential equation of fourth order are

asked Nov 30, 2012 by sreemathi.v

1 answer

The number of arbitrary constants in the particular solution of a differential equation of third order are

asked Nov 30, 2012 by sreemathi.v

1 answer

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b $\large\frac{x}{a}+\frac{y}{b}=1$

asked Nov 30, 2012 by sreemathi.v

1 answer

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.$y^2=a(b^2-x^2)$

asked Nov 30, 2012 by sreemathi.v

1 answer

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b. $y=a\: e^{3x}+b\: e^{-2x}$

asked Nov 30, 2012 by sreemathi.v

1 answer

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b $y=e^{2x}(a+bx)$

asked Nov 30, 2012 by sreemathi.v

1 answer

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b $y=e^x(a\;\cos x+b\;\sin x)$

asked Nov 30, 2012 by sreemathi.v

1 answer

Form the differential equation of the family of circles touching the \(y\) - axis at origin.

asked Nov 30, 2012 by sreemathi.v

1 answer

Form the differential equation of the family of parabolas having vertex at origin at axis along positive y-axis.

asked Nov 30, 2012 by sreemathi.v

1 answer

Form the differential equation of the family of ellipses having foci on $y$-axis and centre at origin.

asked Nov 30, 2012 by sreemathi.v

1 answer

Form the differential equation of the family of hyperbolas having foci on $x$-axis and centre at origin.

asked Nov 30, 2012 by sreemathi.v

1 answer

Form the differential equation of the family of circles having centre on $y$-axis and radius $3$ units.

asked Nov 30, 2012 by sreemathi.v

2 answers

Which of the following differential equations has $y\;=\;c_1e^x+c_2e^{-x}$ as the general solution?

asked Nov 30, 2012 by sreemathi.v

1 answer

Which of the following differential equations has $y = x$ as one of its particular solution?

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $\large\frac{dy}{dx}=\frac{1-\cos x}{1+\cos x}$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $\large\frac{dy}{dx} $$=\sqrt {4-y^2} \; (-2\lt y \lt 2) $

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $\large\frac{dy}{dx}$$+y=1(y\neq1)$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $\sec^2x\;\tan y\;dx+\sec^2y\;\tan x\;dy=0$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $(e^x+e^{-x})\;dy-(e^x-e^{-x})\;dx=0$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $\large\frac{dy}{dx}$$=(1+x^2)(1+y^2)$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $y\;\log\: y\;dx-x\;dy=0$

asked Nov 30, 2012 by sreemathi.v

1 answer

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