Advertisements
Advertisements
Question
Solve the differential equation: y dx + (x – y2)dy = 0
Solution
y dx + (x – y2)dy = 0
Reducing the given differential equation to the form `(dx)/(dy)` + Px = Q we get, `(dx)/(dy) + x/y` = y
I.F = `e^(intPdy)`
= `e^(int 1/y dy)`
= elog y
= y
The general solution is given by
x · IF = `int "Q" * "IF" "dy"`
⇒ xy = `int "y"^2 "dy"`
⇒ xy = `"y"^3/3 + C`, which is the required general solution
APPEARS IN
RELATED QUESTIONS
Find the differential equation representing the family of curves v=A/r+ B, where A and B are arbitrary constants.
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.
`x/a + y/b = 1`
Solve the differential equation `ye^(x/y) dx = (xe^(x/y) + y^2)dy, (y != 0)`
The general solution of a differential equation of the type `dx/dy + P_1 x = Q_1` is ______.
The general solution of the differential equation ex dy + (y ex + 2x) dx = 0 is ______.
Find the differential equation of all the circles which pass through the origin and whose centres lie on x-axis.
Show that y = C x + 2C2 is a solution of the differential equation \[2 \left( \frac{dy}{dx} \right)^2 + x\frac{dy}{dx} - y = 0.\]
Show that y2 − x2 − xy = a is a solution of the differential equation \[\left( x - 2y \right)\frac{dy}{dx} + 2x + y = 0.\]
Verify that y = A cos x + sin x satisfies the differential equation \[\cos x\frac{dy}{dx} + \left( \sin x \right)y=1.\]
Find the differential equation corresponding to y = ae2x + be−3x + cex where a, b, c are arbitrary constants.
Show that the differential equation of all parabolas which have their axes parallel to y-axis is \[\frac{d^3 y}{d x^3} = 0.\]
\[\frac{dy}{dx} = x^2 e^x\]
\[\frac{dy}{dx} - x \sin^2 x = \frac{1}{x \log x}\]
\[(\tan^2 x + 2\tan x + 5)\frac{dy}{dx} = 2(1+\tan x)\sec^2x\]
\[\frac{dy}{dx} = \sin^3 x \cos^2 x + x e^x\]
x cos2 y dx = y cos2 x dy
(1 − x2) dy + xy dx = xy2 dx
A solution of the differential equation `("dy"/"dx")^2 - x "dy"/"dx" + y` = 0 is ______.
Find the general solution of the following differential equation:
`x (dy)/(dx) = y - xsin(y/x)`
The general solution of the differential equation `(dy)/(dx) + x/y` = 0 is
General solution of tan 5θ = cot 2θ is
Solution of the equation 3 tan(θ – 15) = tan(θ + 15) is
The general solution of the differential equation of the type `(dx)/(dy) + p_1y = theta_1` is
The general solution of the differential equation `(ydx - xdy)/y` = 0
The general solution of the differential equation `x^xdy + (ye^x + 2x) dx` = 0
Find the general solution of differential equation `(dy)/(dx) = (1 - cosx)/(1 + cosx)`
The general solution of the differential equation y dx – x dy = 0 is ______.
