Internal problem ID [4151]
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)]`]]
\[ \boxed {\left (-x^{2}+1\right ) {y^{\prime }}^{2}+2 x y y^{\prime }=-4 x^{2}} \]
✓ Solution by Maple
Time used: 0.282 (sec). Leaf size: 46
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 \left (x \right ) = -2 \sqrt {-x^{2}+1} y \left (x \right ) = 2 \sqrt {-x^{2}+1} y \left (x \right ) = -c_{1} +c_{1} x^{2}-\frac {1}{c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 0.35 (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*}