What is the solution for (dy)/(dt)+0.4ty=5t,y(0)=6 ?

The solution for (dy)/(dt)+0.4ty=5t,y(0)=6 is y=12.5-(6.5)/(e^{0.2t^2)}

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(dy)/(dt)+0.4ty=5t,y(0)=6

\frac{d y}{d t} + 0.4 t y = 5 t, y (0) = 6

y = 12.5 - \frac{6.5}{e ^{0.2 t^{2}}}

Solution steps

\frac{d y}{d t} + 0.4 t y = 5 t

Solve linear ODE:

y = 12.5 - \frac{6.5}{e ^{0.2 t^{2}}}

y = 12.5 - \frac{6.5}{e ^{0.2 t^{2}}}

What is the solution for (dy)/(dt)+0.4ty=5t,y(0)=6 ?
The solution for (dy)/(dt)+0.4ty=5t,y(0)=6 is y=12.5-(6.5)/(e^{0.2t^2)}