What is the solution for (dy)/(dt)=3t^2y+(4t+1)e^{t^3} ?

The solution for (dy)/(dt)=3t^2y+(4t+1)e^{t^3} is y=2e^{t^3}t^2+e^{t^3}t+c_{1}e^{t^3}

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(dy)/(dt)=3t^2y+(4t+1)e^{t^3}

\frac{d y}{d t} = 3 t^{2} y + (4 t + 1) e^{t^{3}}

y = 2 e^{t^{3}} t^{2} + e^{t^{3}} t + c_{1} e^{t^{3}}

Solution steps

\frac{d y}{d t} = 3 t^{2} y + (4 t + 1) e^{t^{3}}

Solve linear ODE:

y = 2 e^{t^{3}} t^{2} + e^{t^{3}} t + c_{1} e^{t^{3}}

y = 2 e^{t^{3}} t^{2} + e^{t^{3}} t + c_{1} e^{t^{3}}

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What is the solution for (dy)/(dt)=3t^2y+(4t+1)e^{t^3} ?
The solution for (dy)/(dt)=3t^2y+(4t+1)e^{t^3} is y=2e^{t^3}t^2+e^{t^3}t+c_{1}e^{t^3}