Internal problem ID [4212]
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)]`]]
\[ \boxed {y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+2 y^{2}=x^{2}-a} \]
✓ Solution by Maple
Time used: 0.093 (sec). Leaf size: 83
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 \left (x \right ) = -\frac {\sqrt {4 x^{2}-2 a}}{2} y \left (x \right ) = \frac {\sqrt {4 x^{2}-2 a}}{2} y \left (x \right ) = -\frac {\sqrt {-8 c_{1}^{2}+16 c_{1} x -4 x^{2}-2 a}}{2} y \left (x \right ) = \frac {\sqrt {-8 c_{1}^{2}+16 c_{1} x -4 x^{2}-2 a}}{2} \end{align*}
✓ Solution by Mathematica
Time used: 0.744 (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*}