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

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

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

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

y = e^{x} + x + c_{1}, y = - e^{x} + x + c_{1}

Solution steps

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

Solve separable ODE:

y = e^{x} + x + c_{1}, y = - e^{x} + x + c_{1}

y = e^{x} + x + c_{1}, y = - e^{x} + x + c_{1}

x \to - \infty lim (4 x)

\int \frac{1}{3 - 2 x} d x

\int \frac{1}{1 + 4 x ^{2}} d x

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

\int_{0}^{4} \frac{1}{x ^{2} - 6 x + 5} d x

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