How to find the solution of ode y”-9y’+20y=e^xcos(x) satisfying y(0)=0 y'(0)=0 by variation of parameters method

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 corresponding homogeneous eqn of (1) \[y^{\prime\prime}-9y^\prime+20y=0\] It’s characteristics equation is \[m^2-9m+20=0\] \[m^2-5m-4m+20=0\]…

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