What is the solution for y^{''}+3y^'-54y=-174t+108t^2 ?

The solution for y^{''}+3y^'-54y=-174t+108t^2 is y=c_{1}e^{6t}+c_{2}e^{-9t}-2t^2+3t+5/54

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y^{''}+3y^'-54y=-174t+108t^2

y^{^{''}} + 3 y^{^{'}} - 54 y = - 174 t + 108 t^{2}

y = c_{1} e^{6 t} + c_{2} e^{- 9 t} - 2 t^{2} + 3 t + \frac{5}{54}

Solution steps

y^{''} (t) + 3 y^{'} (t) - 54 y = - 174 t + 108 t^{2}

Solve linear ODE:

y = c_{1} e^{6 t} + c_{2} e^{- 9 t} - 2 t^{2} + 3 t + \frac{5}{54}

y = c_{1} e^{6 t} + c_{2} e^{- 9 t} - 2 t^{2} + 3 t + \frac{5}{54}

2 y^{^{''}} + 5 y^{^{'}} + 3 y = \frac{1}{4} ln (x + 1)

y^{^{''}} + 9 y = 17 sec^{2} (3 t)

y^{^{''}} + 4 y^{^{'}} + 8 y = 8 x^{2} + 8 x + 1

y^{^{''''}} + 2 y^{^{''}} + 1 = 7 sin (t)

(4 d^{2} - 4 d + 1) y = 100

What is the solution for y^{''}+3y^'-54y=-174t+108t^2 ?
The solution for y^{''}+3y^'-54y=-174t+108t^2 is y=c_{1}e^{6t}+c_{2}e^{-9t}-2t^2+3t+5/54