Internal problem ID [12421]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 4.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_rational]
\[ \boxed {x y \left (-{y^{\prime }}^{2}+1\right )-\left (x^{2}-y^{2}-a^{2}\right ) y^{\prime }=0} \]
✗ Solution by Maple
dsolve(x*y(x)*(1-diff(y(x),x)^2)=(x^2-y(x)^2-a^2)*diff(y(x),x),y(x), singsol=all)
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.612 (sec). Leaf size: 75
DSolve[x*y[x]*(1-y'[x]^2)==(x^2-y[x]^2-a^2)*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {c_1 \left (x^2-\frac {a^2}{1+c_1}\right )} \\ y(x)\to -i (a-x) \\ y(x)\to i (a-x) \\ y(x)\to -i (a+x) \\ y(x)\to i (a+x) \\ \end{align*}