What is the solution for y^{''}+5y^'+6y=3t^2+4 ?

The solution for y^{''}+5y^'+6y=3t^2+4 is y=c_{1}e^{-2t}+c_{2}e^{-3t}+(t^2)/2-(5t)/6+43/36

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y^{''}+5y^'+6y=3t^2+4

y^{^{''}} + 5 y^{^{'}} + 6 y = 3 t^{2} + 4

y = c_{1} e^{- 2 t} + c_{2} e^{- 3 t} + \frac{t ^{2}}{2} - \frac{5 t}{6} + \frac{43}{36}

Solution steps

y^{''} (t) + 5 y^{'} (t) + 6 y = 3 t^{2} + 4

Solve linear ODE:

y = c_{1} e^{- 2 t} + c_{2} e^{- 3 t} + \frac{t ^{2}}{2} - \frac{5 t}{6} + \frac{43}{36}

y = c_{1} e^{- 2 t} + c_{2} e^{- 3 t} + \frac{t ^{2}}{2} - \frac{5 t}{6} + \frac{43}{36}

y^{^{''}} + y = sec^{3} (x), y (0) = 1, y^{^{'}} (0) = \frac{1}{2}

y^{^{''}} - y = x^{2}

y^{^{''}} + y = 2, y (0) = 2, y^{^{'}} (0) = 3

y^{^{''}} - y = \frac{4 e ^{- x}}{1 - e ^{- 2 x}}

y^{^{''}} - 2 y^{^{'}} + y = x^{\frac{1}{3}} e^{x}

What is the solution for y^{''}+5y^'+6y=3t^2+4 ?
The solution for y^{''}+5y^'+6y=3t^2+4 is y=c_{1}e^{-2t}+c_{2}e^{-3t}+(t^2)/2-(5t)/6+43/36