Internal problem ID [3702]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 33
Problem number: 977.
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}+2 y y^{\prime } x +a -y^{2}=0} \end {gather*}
✗ Solution by Maple
dsolve(y(x)^2*diff(y(x),x)^2+2*x*y(x)*diff(y(x),x)+a-y(x)^2 = 0,y(x), singsol=all)
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.518 (sec). Leaf size: 61
DSolve[y[x]^2 (y'[x])^2+2 x y[x] y'[x]+a-y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {a+c_1 (-2 x+c_1)} \\ y(x)\to \sqrt {a+c_1 (-2 x+c_1)} \\ y(x)\to -\sqrt {a} \\ y(x)\to \sqrt {a} \\ \end{align*}