Internal problem ID [3704]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 33
Problem number: 979.
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 x y^{\prime } y+a -x^{2}+2 y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.134 (sec). Leaf size: 145
dsolve(y(x)^2*diff(y(x),x)^2-2*x*y(x)*diff(y(x),x)+a-x^2+2*y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {4 x^{2}-2 a}}{2} \\ y \relax (x ) = \frac {\sqrt {4 x^{2}-2 a}}{2} \\ y \relax (x ) = \sqrt {-2 \sqrt {a +2 c_{1}}\, x -c_{1}-x^{2}-a} \\ y \relax (x ) = \sqrt {2 \sqrt {a +2 c_{1}}\, x -c_{1}-x^{2}-a} \\ y \relax (x ) = -\sqrt {-2 \sqrt {a +2 c_{1}}\, x -c_{1}-x^{2}-a} \\ y \relax (x ) = -\sqrt {2 \sqrt {a +2 c_{1}}\, x -c_{1}-x^{2}-a} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.669 (sec). Leaf size: 63
DSolve[y[x]^2 (y'[x])^2-2 x y[x] y'[x]+a -x^2+2 y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-\frac {a}{2}-x^2+4 c_1 x-2 c_1{}^2} \\ y(x)\to \sqrt {-\frac {a}{2}-x^2+4 c_1 x-2 c_1{}^2} \\ \end{align*}