What is the solution for y^{''}-3y^'+2y=4e^{2t},y(0)=-3,y^'(0)=5 ?

The solution for y^{''}-3y^'+2y=4e^{2t},y(0)=-3,y^'(0)=5 is y=4e^{2t}-7e^t+4e^{2t}t

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y^{''}-3y^'+2y=4e^{2t},y(0)=-3,y^'(0)=5

y^{^{''}} - 3 y^{^{'}} + 2 y = 4 e^{2 t}, y (0) = - 3, y^{^{'}} (0) = 5

y = 4 e^{2 t} - 7 e^{t} + 4 e^{2 t} t

Solution steps

y^{''} (t) - 3 y^{'} (t) + 2 y = 4 e^{2 t}

Solve linear ODE:

y = 4 e^{2 t} - 7 e^{t} + 4 e^{2 t} t

y = 4 e^{2 t} - 7 e^{t} + 4 e^{2 t} t

What is the solution for y^{''}-3y^'+2y=4e^{2t},y(0)=-3,y^'(0)=5 ?
The solution for y^{''}-3y^'+2y=4e^{2t},y(0)=-3,y^'(0)=5 is y=4e^{2t}-7e^t+4e^{2t}t