Question

For the differential equation, find the general solution:

`dy/dx + y/x = x^2`

Answer 1

This is a linear differential equation of the form `dy/dx + y/x` + Py = Q.

Here P = `1/x` and Q = x²

∴ I.F. = `e^(int P dx) = e^(int 1/x dx) = e^(log x) = x`

Hence, the general solution of the differential equation

`y × I.F. = int Q xx I.F. dx + C`

`y * x = int x^2 * x + C`

xy = `int x^3 + C`

xy = `x^4/4 + C`