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}) \cdot 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}) \cdot 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}

\frac{7}{x}

y^{^{''}} + y = (x^{2} + x) sin (x)

3 sec (x) - 7 x

x \to 8 lim (\frac{2 + 8}{2 ( 8 )})

n = 1 \sum \infty \frac{1}{n + 2}

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