50.8.14 problem 2(f)

Internal problem ID [7930]
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 : 2(f)
Date solved : Monday, January 27, 2025 at 03:33:00 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 40

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

\[ y = \operatorname {RootOf}\left (\int _{}^{\textit {\_Z}}\frac {2 \textit {\_a}^{2}-1}{2 \textit {\_a}^{3}+2 \textit {\_a}^{2}-\textit {\_a} +1}d \textit {\_a} +\ln \left (x \right )+c_{1} \right ) x \]

✓ Solution by Mathematica

Time used: 0.114 (sec). Leaf size: 80

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

\[ \text {Solve}\left [\text {RootSum}\left [2 \text {$\#$1}^3+2 \text {$\#$1}^2-\text {$\#$1}+1\&,\frac {2 \text {$\#$1}^2 \log \left (\frac {y(x)}{x}-\text {$\#$1}\right )-\log \left (\frac {y(x)}{x}-\text {$\#$1}\right )}{6 \text {$\#$1}^2+4 \text {$\#$1}-1}\&\right ]=-\log (x)+c_1,y(x)\right ] \]