Internal problem ID [8243]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 663.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {2 a +x^{2} \sqrt {-y^{2}+4 a x}}{y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.011 (sec). Leaf size: 27
dsolve(diff(y(x),x) = (2*a+x^2*(-y(x)^2+4*a*x)^(1/2))/y(x),y(x), singsol=all)
\[ -\sqrt {-y \relax (x )^{2}+4 a x}-\frac {x^{3}}{3}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 1.886 (sec). Leaf size: 137
DSolve[y'[x] == (2*a + x^2*Sqrt[4*a*x - y[x]^2])/y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {147456 a^7 x-\left (-64 a^3 x^3+e^{c_1}\right ){}^2}}{192 a^3} \\ y(x)\to \frac {\sqrt {147456 a^7 x-\left (-64 a^3 x^3+e^{c_1}\right ){}^2}}{192 a^3} \\ y(x)\to -\frac {\sqrt {a^6 x \left (36 a-x^5\right )}}{3 a^3} \\ y(x)\to \frac {\sqrt {a^6 x \left (36 a-x^5\right )}}{3 a^3} \\ \end{align*}