Internal problem ID [2363]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 39, page 179
Problem number: 32.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{2}-2 x y y^{\prime }+{y^{\prime }}^{2} \left (x^{2}-1\right )=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve(y(x)^2-2*diff(y(x),x)*x*y(x)+diff(y(x),x)^2*(x^2-1)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= c_{1} \left (x -1\right ) \\ y \left (x \right ) &= c_{1} \left (x +1\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.106 (sec). Leaf size: 26
DSolve[y[x]^2-2*y'[x]*x*y[x]+y'[x]^2*(x^2-1)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 (x-1) \\ y(x)\to c_1 (x+1) \\ y(x)\to 0 \\ \end{align*}