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

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

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(dy)/(dx)=e^{x+y}+(e^yx)/(1+x^2)

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

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

Solution steps

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

Solve separable ODE:

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

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

sec^{2} (x) y^{^{'}} = - csc (y)

y^{^{'}} = e^{x - y}, y (0) = 1

(y x^{2} - 4 y - (x^{2} - 4)) d x + d y = 0

y^{^{'}} = 7 y^{- 2}, y (0) = 3

(3 + x^{2}) d y = 2 x y d x

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