What is the solution for xy^2dx+e^xdy=0,y= 1/2 ?

The solution for xy^2dx+e^xdy=0,y= 1/2 is y=-(e^x)/(x+1+c_{1)e^x}

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xy^2dx+e^xdy=0,y= 1/2

x y^{2} d x + e^{x} d y = 0, y = \frac{1}{2}

y = - \frac{e ^{x}}{x + 1 + c _{1} e ^{x}}

Solution steps

x y^{2} d x + e^{x} d y = 0

Solve separable ODE:

y = - \frac{e ^{x}}{x + 1 + c _{1} e ^{x}}

y = - \frac{e ^{x}}{x + 1 + c _{1} e ^{x}}

x y^{^{'}} = y, y (a) = b

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

y^{^{'}} = e^{3 x - 2 y} + x^{2} e^{- 2 y}

\frac{d t}{d x} + \frac{3}{x} = - \frac{1}{x ^{2}}

\frac{d y}{d x} = 0.06 - \frac{y}{1350}

What is the solution for xy^2dx+e^xdy=0,y= 1/2 ?
The solution for xy^2dx+e^xdy=0,y= 1/2 is y=-(e^x)/(x+1+c_{1)e^x}