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Recent questions tagged ch9

When the interest is compounded continuously, the amount of money invested increases at a rate proportional to its size. If Rs.1000 is invested at 10% compounded continuously, in how many years will the original investment double itself?

asked Feb 4, 2013 by meena.p

0 answers

Solve: \[\frac{xdx+ydy}{xdy-ydx}=\sqrt{\frac{a^2-x^2-y^2}{x^2+y^2}}\] (Hint : take $ x=r\cos \theta,y=r \sin \theta,$ so that $x^2+y^2=r^2)$

asked Feb 4, 2013 by meena.p

0 answers

Solve:\[\frac{dy}{dx}=\frac{x^2+y^2+1}{2xy},\;where\; y(1)=1\]

asked Feb 4, 2013 by meena.p

0 answers

Solve:\[(x^3-3xy^2)dx=(y^3-3x^2y)dy\]

asked Feb 4, 2013 by meena.p

0 answers

Solve:\[\frac{dy}{dx}=\frac{y^2+y+1}{x^2+x+1}=0.\]

asked Feb 4, 2013 by meena.p

0 answers

Solve the differential equation :\[(x^2y+y^2x)dy=(x^3+y^3)dx\]

asked Feb 4, 2013 by meena.p

0 answers

Solve:\[\sqrt{1-y^2}dx=[\sin^{-1}y-x]dy\]

asked Feb 4, 2013 by meena.p

0 answers

Solve:\[(x^3-3xy^2)dx=(y^3-3x^2y)dx\]

asked Feb 4, 2013 by meena.p

0 answers

Solve:\[(x^3y^3+xy)\frac{dy}{dx}=1\]

asked Feb 4, 2013 by meena.p

0 answers

Solve:\[\frac{dy}{dx}=\cos ^3x\sin^4x+x\sqrt {2x+1}\]

asked Feb 4, 2013 by meena.p

0 answers

Solve:\[\bigg[x\sqrt {x^2+y^2}-y^2\bigg]dx+xydy=0\]

asked Feb 4, 2013 by meena.p

0 answers

Solve:\[ydx-(x+2y)^2dy=0\]

asked Feb 4, 2013 by meena.p

1 answer

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

asked Feb 4, 2013 by meena.p

0 answers

Solve:\[(x+y)^2\frac{dy}{dx}=a^2\]

asked Feb 4, 2013 by meena.p

0 answers

Solve:\[(x+y+1)\frac{dy}{dx}=1\]

asked Feb 4, 2013 by meena.p

0 answers

Show that $ Ax^2+By^2=1$ is a solution of the diff. equation. $ x\bigg[y\bigg(\Large\frac{d^2y}{dx^2}\bigg)+\bigg(\frac{dy}{dx}\bigg)^2\bigg]=y \frac{dy}{dx}$

asked Feb 4, 2013 by meena.p

0 answers

Form the differential equation of circles represented by \[(x-\alpha)^2+(y-\beta)^2=r^2\; by \;eliminating\;\alpha\;and\;\beta\]

asked Feb 4, 2013 by meena.p

0 answers

Write the order and degree of the diff. equation $ \bigg(\large\frac{d^2y}{dx^2}\bigg)^{2/3}=\bigg(y+\frac{dy}{dx}\bigg)^{1/2}$

asked Feb 4, 2013 by meena.p

0 answers

Form the differential equation of the family of curves represented by the equation $ (x+a)^2-2y^2=a^2$

asked Feb 4, 2013 by meena.p

0 answers

Write the order and degree of the differential equation.$ \bigg[1+(y')^2\bigg]^{3/2}=y''$

asked Feb 4, 2013 by meena.p

0 answers

True-or-False: The differential equation of all non horizontal lines in a plane is $\large\frac{d^2y}{dy^2}$$=0$.

asked Jan 21, 2013 by sreemathi.v

1 answer

True-or-False: Solution of $x\frac{dy}{dx} - y = x\tan\frac{y}{x}$ is $\sin\bigg(\frac{y}{x}\bigg)=kx$.

asked Jan 21, 2013 by sreemathi.v

1 answer

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

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