Internal problem ID [8823]
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)]`]]
\[ \boxed {y^{2} {y^{\prime }}^{2}-4 a y y^{\prime }+y^{2}=-4 a^{2}+4 x a} \]
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 72
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 \left (x \right ) &= -2 \sqrt {a x} \\ y \left (x \right ) &= 2 \sqrt {a x} \\ y \left (x \right ) &= \sqrt {4 a x -c_{1}^{2}+2 c_{1} x -x^{2}} \\ y \left (x \right ) &= -\sqrt {-x^{2}+\left (4 a +2 c_{1} \right ) x -c_{1}^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.644 (sec). Leaf size: 85
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 {16 a^3 x-4 a^2 x^2-4 a c_1 x-c_1{}^2}}{2 a} \\ y(x)\to \frac {\sqrt {16 a^3 x-4 a^2 x^2-4 a c_1 x-c_1{}^2}}{2 a} \\ \end{align*}