What is the solution for y^{''}+9y=e^t,y(0)=0,y^'(0)=0 ?

The solution for y^{''}+9y=e^t,y(0)=0,y^'(0)=0 is y=-1/10 cos(3t)-1/30 sin(3t)+1/10 e^t

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y^{''}+9y=e^t,y(0)=0,y^'(0)=0

y^{^{''}} + 9 y = e^{t}, y (0) = 0, y^{^{'}} (0) = 0

y = - \frac{1}{10} cos (3 t) - \frac{1}{30} sin (3 t) + \frac{1}{10} e^{t}

Solution steps

y^{''} (t) + 9 y = e^{t}

Solve linear ODE:

y = - \frac{1}{10} cos (3 t) - \frac{1}{30} sin (3 t) + \frac{1}{10} e^{t}

y = - \frac{1}{10} cos (3 t) - \frac{1}{30} sin (3 t) + \frac{1}{10} e^{t}

What is the solution for y^{''}+9y=e^t,y(0)=0,y^'(0)=0 ?
The solution for y^{''}+9y=e^t,y(0)=0,y^'(0)=0 is y=-1/10 cos(3t)-1/30 sin(3t)+1/10 e^t