Internal problem ID [4156]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 31
Problem number: 920.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]
\[ \boxed {\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }=-x^{2}} \]
✓ Solution by Maple
Time used: 1.39 (sec). Leaf size: 51
dsolve((a^2-x^2)*diff(y(x),x)^2+2*x*y(x)*diff(y(x),x)+x^2 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \sqrt {a^{2}-x^{2}} \\ y \left (x \right ) &= -\sqrt {a^{2}-x^{2}} \\ y \left (x \right ) &= c_{1} x^{2}-c_{1} a^{2}-\frac {1}{4 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.417 (sec). Leaf size: 67
DSolve[(a^2-x^2) (y'[x])^2+2 x y[x] y'[x]+x^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {a^2-x^2+c_1{}^2}{2 c_1} \\ y(x)\to \text {Indeterminate} \\ y(x)\to -\sqrt {a^2-x^2} \\ y(x)\to \sqrt {a^2-x^2} \\ \end{align*}