What is the solution for y^'-(3/t)*y=2t^3*e^{(2t)},y(1)=0 ?

The solution for y^'-(3/t)*y=2t^3*e^{(2t)},y(1)=0 is y=e^{2t}t^3-e^2t^3

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y^'-(3/t)y=2t^3e^{(2t)},y(1)=0

y^{^{'}} - (\frac{3}{t}) \cdot y = 2 t^{3} \cdot e^{(2 t)}, y (1) = 0

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

Solution steps

y^{'} (t) - (\frac{3}{t}) \cdot y = 2 t^{3} \cdot 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}

What is the solution for y^'-(3/t)*y=2t^3*e^{(2t)},y(1)=0 ?
The solution for y^'-(3/t)*y=2t^3*e^{(2t)},y(1)=0 is y=e^{2t}t^3-e^2t^3