Internal problem ID [4210]
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)]`]]
\[ \boxed {y^{2} {y^{\prime }}^{2}+2 x y y^{\prime }-y^{2}=-a} \]
✓ Solution by Maple
Time used: 0.266 (sec). Leaf size: 57
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)
\begin{align*} y \left (x \right ) &= \sqrt {-x^{2}+a} \\ y \left (x \right ) &= -\sqrt {-x^{2}+a} \\ y \left (x \right ) &= \sqrt {c_{1}^{2}-2 c_{1} x +a} \\ y \left (x \right ) &= -\sqrt {c_{1}^{2}-2 c_{1} x +a} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.569 (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*}