Question

Find the general solution: $\frac {dy}{dx}+\frac yx=x^2$

Answer 1

The given differential equation is:

$\frac {dy}{dx}$+ py = Q (where p=$\frac 1x$ and Q=x2)

Now, I.F = e∫pdx = e\int$$\frac 1xdx = elog x = x.

The solution of the given differential equation is given by the relation,

y(I.F.) = $\int$(Q×I.F.)dx+C

$⇒$y(x) = $\int$(x2.x)dx+C

$⇒$xy = $\int$x3dx+C

$⇒$xy = $\frac {x^4}{4}$+C

This is the required solution of the given differential equation.