Question

Solve the differential equation `"dy"/"dx" + y/x` = x².

Answer 1

The equation is of the type `"dy"/"dx" + "Py"` = Q, which is a linear differential equation.

Now I.F. = `int 1/x  "d"x`

= e^logx = x.

Therefore, solution of the given differential equation is

y.x = `int x x^2  "d"x`

i.e. yx = `x^4/4 + "c"`

Hence y = `x^3/4 + "c"/x`.