Recent questions tagged solving-using-separation-of-variables

Find the general solution of $xy' - 2y = x^2$

asked Mar 20, 2014 by balaji.thirumalai

1 answer

Solve : $ x \large\frac{dy}{dx}- \frac{y}{2}$$=x(\sin ^{-1}x) y^5$

asked Feb 6, 2014 by meena.p

1 answer

Find the solution : $ (1+x^4) \large\frac{dy}{dx}$$-4x^3y =(x^5+x) \tan ^{-1} (x^2) \qquad y(1)=\pi$

asked Feb 6, 2014 by meena.p

1 answer

The initial value problem governing the current i following in an RL circuit when a step voltage of magnitude $\in$ is applied to circuit at $t=0$ is given by (R, L, t are constants ) $iR= \large\frac{Ldi}{dt} $$=\in, t > 0, i(0)=0$ Determine limiting value of i as $t \to \infty$

asked Feb 6, 2014 by meena.p

1 answer

Observation show that rate of change of atmosphere pressure P with attitude h is proportional to pressure. Assume that pressure at 6000 meter is half of its value $P_0$ at sea level, find formula for pressure at any height.

asked Feb 6, 2014 by meena.p

1 answer

Find the solution : $y (\log x-1) y dx=x dy $

asked Feb 5, 2014 by meena.p

1 answer

The graph of the function $y=f(x)$ passing through the point $(0,1)$ and satisfy the differential equation $\large\frac{dy}{dx}$$+y \cos x =\cos x $ is such that

asked Feb 5, 2014 by meena.p

1 answer

General solution of differential equation: $r \sin \theta\; d\theta +(r^3 -2 r^2 \cos \theta +\cos \theta)dr=0$

asked Feb 4, 2014 by meena.p

1 answer

General solution of differential equation: $\large\frac{dy}{dx}$$+x \sin 2y=x^3 \cos ^2 y$

asked Feb 4, 2014 by meena.p

1 answer

General solution of differential equation: $x \large\frac{dy}{dx}$$+y=x^3 y^6$

asked Feb 4, 2014 by meena.p

1 answer

General solution of differential equation : $(1+y^2)dx =(\tan^{-1}y -x)dy$

asked Feb 4, 2014 by meena.p

1 answer

General solution of differential equation ; $\large\frac{ydy}{xdx}+\frac{2(x^2+y^2)-1}{(x^2+y^2+1)}=0$

asked Feb 4, 2014 by meena.p

1 answer

General solution of differential equations: $\large\frac{dy}{dx}$$=e^{3x-2y}+x^2e^{-2y}$

asked Feb 4, 2014 by meena.p

1 answer

Differential equation of all circles radius 5, with their centres on the y-axis.

asked Feb 4, 2014 by meena.p

1 answer

Different equation of all parabola with x axis as the axis and $(a,0)$ as the focus

asked Feb 3, 2014 by meena.p

1 answer

Solution of the general equation : $\large\frac{dy}{dx}$$=\cos (x+y) - \sin (x+y) $

asked Feb 3, 2014 by meena.p

1 answer

General solution of differential equation : $ (1-x^2)(1-y)dx -xy (1+y) dy=0$

asked Feb 3, 2014 by meena.p

1 answer

General solution of differential equation : $x^2e^y dy - (x-1) e^x dx=0$

asked Feb 3, 2014 by meena.p

1 answer

General solution of differential equation $x dy -y dx=0$

asked Feb 3, 2014 by meena.p

1 answer

General solution of differential equation : $x dy +y dx=0$

asked Feb 3, 2014 by meena.p

1 answer

2 separate reservation of oil A and B (capacity of $A=2 \times $ capacity of B) are filled completely with oil and oil is released simultaneously from both the reservoirs. The rate of flow of oil out of each reservoir at an instant of time is proportional to the quantity of oil in the reservoir at that time one hour after the oil is released the quantity of oil in reservoir A is 1.5 times the quantity of oil in reservoir B. If the reservoirs have same quantity of oil after $t= \large\frac{\log a}{\log b -\log c}$ then $a+b-c$

asked Feb 3, 2014 by meena.p

1 answer

General solution of differential equations: $e^y dx+(xe^y-2y)dy=0$

asked Feb 3, 2014 by meena.p

1 answer

General solution of differential equation: $\large\frac{xdy}{x^2+y^2} $$+\bigg(1- \large\frac{y}{x^2+y^2} \bigg)$$dx=0$ is

asked Feb 3, 2014 by meena.p

1 answer

If $x= \cos^{-1} \bigg( \large\frac{1}{\sqrt {1+t^2}}\bigg) $ and $\; y= \sin ^{-1} \bigg( \large\frac{1}{\sqrt {1+t^2}}\bigg) $ then $\large\frac{dy}{dx}$

asked Jan 31, 2014 by meena.p

1 answer

Solution of differential equation: $X^2= 1+\large\frac{1}{2} \bigg( \large\frac{x}{y}\bigg)^{-1} \frac{dy}{dx} + \large\frac{\bigg(\Large\frac{x}{y}\bigg)^{-2} \bigg(\Large\frac{dy}{dx}\bigg)^{2}}{4 \times 2 \times 1}+ \large\frac{\bigg(\Large\frac{x}{y}\bigg)^{-3} \bigg(\Large\frac{dy}{dx}\bigg)^{3}}{8 \times 3 \times 2 \times 1}+ \large\frac{\bigg(\Large\frac{x}{y}\bigg)^{-4} \bigg(\Large\frac{dy}{dx}\bigg)^{4}}{16 \times 4 \times 3 \times 2 \times 1}+..........$

asked Jan 31, 2014 by meena.p

1 answer

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