second order ODEs

Question : Find the solution of ode y''-9y'+20y=e^xcos(x) satisfying y(0)=0 y'(0)=0 by variation of parameters method. Solution : \[y^{\prime\prime}-9y^\prime+20y=e^x\cos{\left(x\right)} \] (1) To find complementary solution of ode (1) we solve…

Question : Find the solution of ode y''-9y'+20y=0 by variation of parameters method Solution : \[y^{\prime\prime}-9y^\prime+20y=e^x\cos{\left(x\right)} \] (1) To find complementary solution of ode (1) we solve corresponding homogeneous eqn…