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{d}{d x} ((5 x + 8)^{2})

y^{^{''}} + 25 y = 5 csc^{2} (5 t)

\frac{d}{d x} (x^{3 s i n (x)})

\int e^{y t} \cdot sin (k t) d t

(2 t)^{^{'}}

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}