60.2.34 problem 610

Internal problem ID [10621]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 610
Date solved : Monday, January 27, 2025 at 09:18:19 PM
CAS classification : [[_homogeneous, `class D`]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 0.084 (sec). Leaf size: 25

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

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