What is the solution for (dy)/(dt)-3/t y=2t^3e^{2t},y(1)=0 ?

The solution for (dy)/(dt)-3/t y=2t^3e^{2t},y(1)=0 is y=e^{2t}t^3-e^2t^3

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(dy)/(dt)-3/t y=2t^3e^{2t},y(1)=0

\frac{d y}{d t} - \frac{3}{t} y = 2 t^{3} e^{2 t}, y (1) = 0

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

Solution steps

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

Solve linear ODE:

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

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

\int 24 x d x

\frac{d y}{d t} = - k y

9 x - 4 y (x^{2} + 1) (\frac{d y}{d x}) = 0

\int \frac{x}{( x + 4 ) ^{\frac{1}{3}}} d x

f (x) = e^{x} + 1

What is the solution for (dy)/(dt)-3/t y=2t^3e^{2t},y(1)=0 ?
The solution for (dy)/(dt)-3/t y=2t^3e^{2t},y(1)=0 is y=e^{2t}t^3-e^2t^3