Internal problem ID [6253]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven
Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Problems for Review and Discovery. Page
53
Problem number: 1(e).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {y^{\prime }-\frac {x^{2}+y^{2}}{-y^{2}+x^{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(diff(y(x),x)=(x^2+y(x)^2)/(x^2-y(x)^2),y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {RootOf}\left (\int _{}^{\textit {\_Z}}\frac {\textit {\_a}^{2}-1}{\textit {\_a}^{3}+\textit {\_a}^{2}-\textit {\_a} +1}d \textit {\_a} +\ln \left (x \right )+c_{1} \right ) x \]
✓ Solution by Mathematica
Time used: 0.115 (sec). Leaf size: 67
DSolve[y'[x]==(x^2+y[x]^2)/(x^2-y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\text {RootSum}\left [\text {$\#$1}^3+\text {$\#$1}^2-\text {$\#$1}+1\&,\frac {\text {$\#$1} \log \left (\frac {y(x)}{x}-\text {$\#$1}\right )-\log \left (\frac {y(x)}{x}-\text {$\#$1}\right )}{3 \text {$\#$1}-1}\&\right ]=-\log (x)+c_1,y(x)\right ] \]