let K be a non zero constant. Assume p and q are continuous on an interval I. If a exists in the interval I and if b is any real number, let v= g(x) be the unique solution of the initial value problem v' + k p(x) v = k q(x) on I , with g(a) =b . if n does not equal 1 and k=1 -n', prove that a function y = f(x), which is not identically zero on I is a solution of the initial value problem y' + p(x)y = q(x) y^n on I with f(a)^k = b.