What is the solution for (dy)/(dx)=(1+x)(1+y) ?

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

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(dy)/(dx)=(1+x)(1+y)

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

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

Solution steps

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

Solve separable ODE:

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

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

\int \frac{e ^{- x} sin ^{2} ( x )}{2} d x

x \to 0 lim (\frac{sin ( x )}{4 x})

\frac{d}{d x} (A e^{3 x} + 3 A x e^{3 x})

x \to 1 lim (4 x^{5} - 2 x^{4} - 3)

(2, 4), (- 1, - 5)

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