Internal problem ID [8230]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 652.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [`y=_G(x,y')`]
\[ \boxed {y^{\prime }-\frac {2 a +x \sqrt {-y^{2}+4 a x}}{y}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(x),x) = (2*a+x*(-y(x)^2+4*a*x)^(1/2))/y(x),y(x), singsol=all)
\[ -\sqrt {4 a x -y \left (x \right )^{2}}-\frac {x^{2}}{2}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 6.52 (sec). Leaf size: 137
DSolve[y'[x] == (2*a + x*Sqrt[4*a*x - y[x]^2])/y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {4096 a^5 x-\left (-16 a^2 x^2+e^{c_1}\right ){}^2}}{32 a^2} \\ y(x)\to \frac {\sqrt {4096 a^5 x-\left (-16 a^2 x^2+e^{c_1}\right ){}^2}}{32 a^2} \\ y(x)\to -\frac {\sqrt {a^4 x \left (16 a-x^3\right )}}{2 a^2} \\ y(x)\to \frac {\sqrt {a^4 x \left (16 a-x^3\right )}}{2 a^2} \\ \end{align*}