82.12.15 problem Ex. 15

Internal problem ID [18780]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Examples on chapter II at page 29
Problem number : Ex. 15
Date solved : Tuesday, January 28, 2025 at 12:17:05 PM
CAS classification : [_rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.003 (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: 0.306 (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*}