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

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

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e^x(dy)/(dx)=(x+xy^2)

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

y = tan (\frac{- x - 1}{e ^{x}} + c_{1})

Solution steps

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

Solve separable ODE:

y = tan (\frac{- x - 1}{e ^{x}} + c_{1})

y = tan (\frac{- x - 1}{e ^{x}} + c_{1})

y^{^{'}} = \frac{2 x}{1 + 2 y}, y (3) = 0

\frac{d y}{d x} = \frac{x y - x ^{3} y}{1 - y}

x d y - y d x = 0, y (1) = 2

\frac{d y}{d x} = \frac{y}{x}, y (5) = 20

\frac{d y}{d x} = - \frac{3}{7} x^{6} y^{5}

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