What is the solution for y^{''}-2y^'+y=t+1,y(0)=0,y^'(0)=0 ?

The solution for y^{''}-2y^'+y=t+1,y(0)=0,y^'(0)=0 is y=-3e^t+2e^tt+t+3

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y^{''}-2y^'+y=t+1,y(0)=0,y^'(0)=0

y^{^{''}} - 2 y^{^{'}} + y = t + 1, y (0) = 0, y^{^{'}} (0) = 0

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

Solution steps

y^{''} (t) - 2 y^{'} (t) + y = t + 1

Solve linear ODE:

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

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

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What is the solution for y^{''}-2y^'+y=t+1,y(0)=0,y^'(0)=0 ?
The solution for y^{''}-2y^'+y=t+1,y(0)=0,y^'(0)=0 is y=-3e^t+2e^tt+t+3