What is the solution for y^{''}-6y^'+9y=t,y(0)=0,y(0)=1 ?

The solution for y^{''}-6y^'+9y=t,y(0)=0,y(0)=1 is y=-2/27 e^{3t}+c_{2}e^{3t}t+t/9+2/27

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y^{''}-6y^'+9y=t,y(0)=0,y(0)=1

y^{^{''}} - 6 y^{^{'}} + 9 y = t, y (0) = 0, y (0) = 1

y = - \frac{2}{27} e^{3 t} + c_{2} e^{3 t} t + \frac{t}{9} + \frac{2}{27}

Solution steps

y^{''} (t) - 6 y^{'} (t) + 9 y = t

Solve linear ODE:

y = - \frac{2}{27} e^{3 t} + c_{2} e^{3 t} t + \frac{t}{9} + \frac{2}{27}

y = - \frac{2}{27} e^{3 t} + c_{2} e^{3 t} t + \frac{t}{9} + \frac{2}{27}

What is the solution for y^{''}-6y^'+9y=t,y(0)=0,y(0)=1 ?
The solution for y^{''}-6y^'+9y=t,y(0)=0,y(0)=1 is y=-2/27 e^{3t}+c_{2}e^{3t}t+t/9+2/27