15.2.8 problem 8

Internal problem ID [2878]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 6, page 25
Problem number : 8
Date solved : Monday, January 27, 2025 at 06:22:38 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 28

dsolve((x^2+y(x)^2)=x*y(x)*diff(y(x),x),y(x), singsol=all)
 

\begin{align*} y &= \sqrt {2 \ln \left (x \right )+c_1}\, x \\ y &= -\sqrt {2 \ln \left (x \right )+c_1}\, x \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.175 (sec). Leaf size: 36

DSolve[(x^2+y[x]^2)==x*y[x]*D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -x \sqrt {2 \log (x)+c_1} \\ y(x)\to x \sqrt {2 \log (x)+c_1} \\ \end{align*}