8.1.3.9 Higher order differential equations

Problem: Find the homogeneous linear differential equation with constant real coefficients, possibly of a lower order, a) which has the solution \( y_{1}=e^{4 x} \sin 2 x \), b) which has the solution \( y_{1}=x e^{-4 x} \sin 2 x \), c) which has the solutions \( y_{1}=x^{3}, y_{2}=e^{4 x} \sin 2 x \). clip2net.com