What is the solution for (dy)/(dt)=1+t+y+ty ?

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

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(dy)/(dt)=1+t+y+ty

\frac{d y}{d t} = 1 + t + y + t y

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

Solution steps

\frac{d y}{d t} = 1 + t + y + t y

Solve separable ODE:

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

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

\frac{d}{d x} (x^{2} + 2 x - 8)

\frac{\partial}{\partial x} (e^{- x} tan (y))

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\frac{d y}{d x} + 2 y = 50

\frac{d}{d t} (6 sin^{3} (t))

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