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

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

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y(dy)/(dx)=e^{x-y^2}

y \frac{d y}{d x} = e^{x - y^{2}}

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

Solution steps

y \frac{d y}{d x} = e^{x - y^{2}}

Solve separable ODE:

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

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

\frac{d y}{d t} = 1.5 - 0.01 y, y (0) = 5

\frac{d x}{0.5 + 0.8 x} = \frac{d y}{1.5 - 0.8 y}

y^{^{'}} + 4 y = \frac{4}{3}

x \frac{d y}{d x} = \frac{e ^{x}}{e ^{y}}

e^{4 x} e^{2 y} \frac{d x}{d y} - e^{- 3 y} = 0

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