What is the solution for (dy)/(dt)=3y-e^{3t}+6t^2-2 ?

The solution for (dy)/(dt)=3y-e^{3t}+6t^2-2 is y=-e^{3t}t-2t^2-(4t)/3+2/9+c_{1}e^{3t}

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(dy)/(dt)=3y-e^{3t}+6t^2-2

\frac{d y}{d t} = 3 y - e^{3 t} + 6 t^{2} - 2

y = - e^{3 t} t - 2 t^{2} - \frac{4 t}{3} + \frac{2}{9} + c_{1} e^{3 t}

Solution steps

\frac{d y}{d t} = 3 y - e^{3 t} + 6 t^{2} - 2

Solve linear ODE:

y = - e^{3 t} t - 2 t^{2} - \frac{4 t}{3} + \frac{2}{9} + c_{1} e^{3 t}

y = - e^{3 t} t - 2 t^{2} - \frac{4 t}{3} + \frac{2}{9} + c_{1} e^{3 t}

\frac{\partial}{\partial x} (\frac{x}{x ^{2} + 2 x y + y ^{2}})

\frac{d}{d x} ((4 x - 8)^{2})

\int_{0}^{x} 3 e^{- 3 x} d x

x \to \infty lim (13 x)

\int x^{9} x^{5} + 7 d x

What is the solution for (dy)/(dt)=3y-e^{3t}+6t^2-2 ?
The solution for (dy)/(dt)=3y-e^{3t}+6t^2-2 is y=-e^{3t}t-2t^2-(4t)/3+2/9+c_{1}e^{3t}