Internal problem ID [3643]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 31
Problem number: 915.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(y)]]]
Solve \begin {gather*} \boxed {\left (1-x^{2}\right ) \left (y^{\prime }\right )^{2}+2 y y^{\prime } x +4 x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 3.063 (sec). Leaf size: 33
dsolve((-x^2+1)*diff(y(x),x)^2+2*x*y(x)*diff(y(x),x)+4*x^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -c_{1}+c_{1} x^{2}-\frac {1}{c_{1}} \\ y \relax (x ) = \sqrt {x -1}\, \sqrt {x +1}\, c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.357 (sec). Leaf size: 63
DSolve[(1-x^2) (y'[x])^2+2 x y[x] y'[x]+4 x^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-4 x^2+4+c_1{}^2}{2 c_1} \\ y(x)\to \text {Indeterminate} \\ y(x)\to -2 \sqrt {1-x^2} \\ y(x)\to 2 \sqrt {1-x^2} \\ \end{align*}