75.7.22 problem 197

Internal problem ID [16815]
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
Date solved : Tuesday, January 28, 2025 at 09:33:41 AM
CAS classification : [_rational, _Bernoulli]

\begin{align*} x^{2}+y^{2}+1-2 x y y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (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 &= \sqrt {c_{1} x +x^{2}-1} \\ y &= -\sqrt {c_{1} x +x^{2}-1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.300 (sec). Leaf size: 37

DSolve[( x^2+y[x]^2+1)-( 2*x*y[x])*D[y[x],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*}