Internal problem ID [9587]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime }-f \left (\frac {y}{x}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(y(x),x)=f(y(x)/x),y(x), singsol=all)
\[ y \relax (x ) = \RootOf \left (-\left (\int _{}^{\textit {\_Z}}\frac {1}{f \left (\textit {\_a} \right )-\textit {\_a}}d \textit {\_a} \right )+\ln \relax (x )+c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 0.067 (sec). Leaf size: 33
DSolve[y'[x]==f[y[x]/x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{K[1]-f(K[1])}dK[1]=-\log (x)+c_1,y(x)\right ] \]