Internal problem ID [15133]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 11. Singular solutions of differential equations. Exercises page 92
Problem number: 271.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{2} {y^{\prime }}^{2}+y^{2}=1} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 51
dsolve(y(x)^2*diff(y(x),x)^2+y(x)^2=1,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -1 \\ y \left (x \right ) &= 1 \\ y \left (x \right ) &= \sqrt {-c_{1}^{2}+2 c_{1} x -x^{2}+1} \\ y \left (x \right ) &= -\sqrt {-\left (x -c_{1} +1\right ) \left (x -c_{1} -1\right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.185 (sec). Leaf size: 119
DSolve[y[x]^2*y'[x]^2+y[x]^2==1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-x^2-2 c_1 x+1-c_1{}^2} \\ y(x)\to \sqrt {-x^2-2 c_1 x+1-c_1{}^2} \\ y(x)\to -\sqrt {-x^2+2 c_1 x+1-c_1{}^2} \\ y(x)\to \sqrt {-x^2+2 c_1 x+1-c_1{}^2} \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}