What is the solution for (dy)/(dx)=(1+x^2)(1+y) ?

The solution for (dy)/(dx)=(1+x^2)(1+y) is y=e^{x+(x^3)/3+c_{1}}-1

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(dy)/(dx)=(1+x^2)(1+y)

\frac{d y}{d x} = (1 + x^{2}) (1 + y)

y = e^{x + \frac{x ^{3}}{3} + c_{1}} - 1

Solution steps

\frac{d y}{d x} = (1 + x^{2}) (1 + y)

Solve separable ODE:

y = e^{x + \frac{x ^{3}}{3} + c_{1}} - 1

y = e^{x + \frac{x ^{3}}{3} + c_{1}} - 1

y^{2} y^{^{'}} = - 2 x y, y (0) = 2

\frac{d y}{d x} = \frac{x - 5}{y}

\frac{d y}{d x} = - \frac{3}{4} x^{4} y^{3}

y^{2} (3 v + 1) d v + y^{2} (- v^{2}) d y = 0

y^{^{'}} = \frac{x ( x + 1 )}{4 y ^{3}}

What is the solution for (dy)/(dx)=(1+x^2)(1+y) ?
The solution for (dy)/(dx)=(1+x^2)(1+y) is y=e^{x+(x^3)/3+c_{1}}-1