Question

Find the general solution of the linear equation of the first order (dy/dx) + p(x)y = q(x), if one particular solution y₁(x) is known.

Answer 1

The given differential equation is

(dy/dx) + p(x)y = q(x)

which is a linear differential equation.

∴ IF = e^{∫p(x) dx} = e^{p(x) x}

Hence, the solution is

y.e^{p(x) x} = ∫(e^p(x)x.q(x)) dx + c