61.1.6 problem 1.1.6

Internal problem ID [12006]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 1, First-Order differential equations
Problem number : 1.1.6
Date solved : Monday, January 27, 2025 at 11:48:09 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 27

dsolve(diff(y(x),x)=f(y(x)/x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.071 (sec). Leaf size: 33

DSolve[D[y[x],x]==f[y[x]/x],y[x],x,IncludeSingularSolutions -> True]
 

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