What is the solution for y^{''}-8y^'+16y=32t+64,y(0)=3,y^'(0)=-3 ?

The solution for y^{''}-8y^'+16y=32t+64,y(0)=3,y^'(0)=-3 is y=-2e^{4t}+3e^{4t}t+2t+5

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y^{''}-8y^'+16y=32t+64,y(0)=3,y^'(0)=-3

y^{^{''}} - 8 y^{^{'}} + 16 y = 32 t + 64, y (0) = 3, y^{^{'}} (0) = - 3

y = - 2 e^{4 t} + 3 e^{4 t} t + 2 t + 5

Solution steps

y^{''} (t) - 8 y^{'} (t) + 16 y = 32 t + 64

Solve linear ODE:

y = - 2 e^{4 t} + 3 e^{4 t} t + 2 t + 5

y = - 2 e^{4 t} + 3 e^{4 t} t + 2 t + 5

y^{^{''}} + 4 y^{^{'}} + 40 y = 12.5 sin (6 t)

y^{^{''}} + 3 y^{^{'}} - 28 y = - 96 t + 56 t^{2}

θ^{^{''}} (t) - θ (t) = t

y^{^{'''}} + y^{^{'}} = sec (x)

y^{^{''}} + 7 y^{^{'}} - 8 y = 13 e^{2 x}, y (0) = 1, y^{^{'}} (0) = 1

What is the solution for y^{''}-8y^'+16y=32t+64,y(0)=3,y^'(0)=-3 ?
The solution for y^{''}-8y^'+16y=32t+64,y(0)=3,y^'(0)=-3 is y=-2e^{4t}+3e^{4t}t+2t+5