Internal problem ID [8068]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 488.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x),G(y)]]]
Solve \begin {gather*} \boxed {y^{2} \left (y^{\prime }\right )^{2}-4 a y y^{\prime }+y^{2}-4 a x +4 a^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 113
dsolve(y(x)^2*diff(y(x),x)^2-4*a*y(x)*diff(y(x),x)+y(x)^2-4*a*x+4*a^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -2 \sqrt {x a} \\ y \relax (x ) = 2 \sqrt {x a} \\ y \relax (x ) = -\frac {\sqrt {-16 a^{4}+32 a^{3} x -16 x^{2} a^{2}+8 c_{1} a^{2}+8 a x c_{1}-c_{1}^{2}}}{4 a} \\ y \relax (x ) = \frac {\sqrt {-16 a^{4}+32 a^{3} x -16 x^{2} a^{2}+8 c_{1} a^{2}+8 a x c_{1}-c_{1}^{2}}}{4 a} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.63 (sec). Leaf size: 83
DSolve[4*a^2 - 4*a*x + y[x]^2 - 4*a*y[x]*y'[x] + y[x]^2*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {4 a^2 x (4 a-x)-4 a c_1 x-c_1{}^2}}{2 a} \\ y(x)\to \frac {\sqrt {4 a^2 x (4 a-x)-4 a c_1 x-c_1{}^2}}{2 a} \\ \end{align*}