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

The solution for (dy)/(dx)=ksqrt(2y+a) is y=(k^2x^2)/2+c_{1}kx+(c_{1}^2)/2-a/2

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(dy)/(dx)=ksqrt(2y+a)

\frac{d y}{d x} = k 2 y + a

y = \frac{k ^{2} x ^{2}}{2} + c_{1} k x + \frac{c _{1}^{2}}{2} - \frac{a}{2}

Solution steps

\frac{d y}{d x} = k 2 y + a

Solve separable ODE:

y = \frac{k ^{2} x ^{2}}{2} + c_{1} k x + \frac{c _{1}^{2}}{2} - \frac{a}{2}

y = \frac{k ^{2} x ^{2}}{2} + c_{1} k x + \frac{c _{1}^{2}}{2} - \frac{a}{2}

(y^{^{'}}) = e^{x} e^{y}

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

(t^{2} + 1) y^{^{'}} = sin (t^{2} + 3 cos (t)) y

\frac{d y}{d x} = cos^{2} (y), \frac{π}{2} < y

\frac{d y}{d x} (\frac{y}{x}) y = (x + c^{1})^{2}

What is the solution for (dy)/(dx)=ksqrt(2y+a) ?
The solution for (dy)/(dx)=ksqrt(2y+a) is y=(k^2x^2)/2+c_{1}kx+(c_{1}^2)/2-a/2