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

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

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

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

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

y^{^{''}} - 4 y^{^{'}} + 8 y = 16 x

(d^{2} + 1) y = x^{3}

y^{^{''}} + 4 y = 8 x^{2} + 9 x

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - y = x e^{x}

y^{^{''}} + y = 8 x

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