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}

x^{2} \frac{d y}{d x} + x y = 3 x

y^{^{'}} = \frac{5 sin ( x )}{sin ( y )}, y (0) = \frac{π}{2}

\frac{d y}{d x} = \frac{3 x ^{2} - 2 x}{2 y + 1}, y (0) = 2

y^{^{'}} = y + y^{2}

y^{^{'}} = t \cdot e^{y}, y (2) = 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)}