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 \frac{x + 5}{x - 2} d x

\int 6 θ cos (θ) d θ

\frac{x + 2}{4 x - 3}

\int \frac{x}{( x ^{2} - 2 x + 5 )} d x

y^{^{'}} = y^{2} - 3 y

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