60.2.22 problem 598

Internal problem ID [10609]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 598
Date solved : Monday, January 27, 2025 at 09:17:48 PM
CAS classification : [[_homogeneous, `class D`]]

\begin{align*} y^{\prime }&=\frac {y+F \left (\frac {y}{x}\right )}{x -1} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 29

dsolve(diff(y(x),x) = (y(x)+F(y(x)/x))/(x-1),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.154 (sec). Leaf size: 45

DSolve[D[y[x],x] == (F[y[x]/x] + y[x])/(-1 + x),y[x],x,IncludeSingularSolutions -> True]
 

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