What is the solution for (dy)/(dt)+8ty=5t ?

The solution for (dy)/(dt)+8ty=5t is y=(e^{-4t^2+c_{1}})/8+5/8

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(dy)/(dt)+8ty=5t

\frac{d y}{d t} + 8 t y = 5 t

y = \frac{e ^{- 4 t^{2} + c_{1}}}{8} + \frac{5}{8}

Solution steps

\frac{d y}{d t} + 8 t y = 5 t

Solve separable ODE:

y = \frac{e ^{- 4 t^{2} + c_{1}}}{8} + \frac{5}{8}

y = \frac{e ^{- 4 t^{2} + c_{1}}}{8} + \frac{5}{8}

\frac{d}{d x} (3 x + x^{2} - 3 x^{3} - x^{4})

arccsc (- 3 t^{2})

y = e^{- 5 x}

\frac{d}{d x} (x - 10 3 x)

\frac{\partial}{\partial x} (x^{2} + y^{2} - x y)

What is the solution for (dy)/(dt)+8ty=5t ?
The solution for (dy)/(dt)+8ty=5t is y=(e^{-4t^2+c_{1}})/8+5/8