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

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

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(dy)/(dx)=((x+2))/(2y)

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

y = \frac{x ^{2}}{2} + 2 x + c_{1}, y = - \frac{x ^{2}}{2} + 2 x + c_{1}

Solution steps

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

Solve separable ODE:

y = \frac{x ^{2}}{2} + 2 x + c_{1}, y = - \frac{x ^{2}}{2} + 2 x + c_{1}

y = \frac{x ^{2}}{2} + 2 x + c_{1}, y = - \frac{x ^{2}}{2} + 2 x + c_{1}

y^{^{'}} = y - 4

(x^{4} + 1) y^{^{'}} + 2 x^{3} y = x^{3}

y^{^{'}} = 2 - 3 y

y^{^{'}} = 8 - y

x \frac{d y}{d x} = e^{4 y + x}, x > 0

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