Question

solution of homogeneous differential equations with variable coefficients

Answer 1

This is a first order linear equation with p(t) = −5 and g(t) = 0. (!) The method used in the above example can be used to solve any second order linear equation of the form y″ + p(t) y′ = g(t), regardless whether its coefficients are constant or nonconstant, or it is ahomogeneous equation or nonhomogeneous.