50.5.21 problem 7(c)

Internal problem ID [7891]
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. Section 1.7. Homogeneous Equations. Page 28
Problem number : 7(c)
Date solved : Monday, January 27, 2025 at 03:31:17 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} y^{\prime }&=\frac {x^{2}-y x}{y^{2} \cos \left (\frac {x}{y}\right )} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 36

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

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

✓ Solution by Mathematica

Time used: 1.098 (sec). Leaf size: 49

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

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {\cos \left (\frac {1}{K[1]}\right ) K[1]^2}{\cos \left (\frac {1}{K[1]}\right ) K[1]^3+K[1]-1}dK[1]=-\log (x)+c_1,y(x)\right ] \]