Solve the given differential equation by undetermined coefficients.y+2y+ y = sin(x)+7 cos(2x)Step 1We are given the following nonhomogeneous differential equation.y+2y+ y = sin(x)+7 cos(2x)To find the general solution, we first find the complementary functionycfor the associated homogenous equationy+2y+ y =0.Then we find a particular solutionypfor the nonhomogeneous equation, which is determined by the form ofg(x)= sin(x)+7 cos(2x).The general solution is then found as the sumy = yc + yp.First, we must find the roots of t