Internal problem ID [15085]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 7, Total differential equations. The integrating factor. Exercises page
61
Problem number: 197.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
\[ \boxed {y^{2}-2 x y y^{\prime }=-x^{2}-1} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 29
dsolve(( x^2+y(x)^2+1)-( 2*x*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \sqrt {c_{1} x +x^{2}-1} \\ y \left (x \right ) &= -\sqrt {c_{1} x +x^{2}-1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.26 (sec). Leaf size: 37
DSolve[( x^2+y[x]^2+1)-( 2*x*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {x^2+c_1 x-1} \\ y(x)\to \sqrt {x^2+c_1 x-1} \\ \end{align*}