What is the solution for y^{''}+5y^'+6y=6t+17,y(0)=3,y^'(0)=-4 ?

The solution for y^{''}+5y^'+6y=6t+17,y(0)=3,y^'(0)=-4 is y=-2e^{-2t}+3e^{-3t}+t+2

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y^{''}+5y^'+6y=6t+17,y(0)=3,y^'(0)=-4

y^{^{''}} + 5 y^{^{'}} + 6 y = 6 t + 17, y (0) = 3, y^{^{'}} (0) = - 4

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

Solution steps

y^{''} (t) + 5 y^{'} (t) + 6 y = 6 t + 17

Solve linear ODE:

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

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

What is the solution for y^{''}+5y^'+6y=6t+17,y(0)=3,y^'(0)=-4 ?
The solution for y^{''}+5y^'+6y=6t+17,y(0)=3,y^'(0)=-4 is y=-2e^{-2t}+3e^{-3t}+t+2