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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

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