83.8.10 problem 11

Internal problem ID [19136]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Misc examples on chapter II at page 25
Problem number : 11
Date solved : Tuesday, January 28, 2025 at 01:05:05 PM
CAS classification : [_rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 29

dsolve(diff(y(x),x)=(x^2+y(x)^2+1)/(2*x*y(x)),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: 0.278 (sec). Leaf size: 37

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