60.1.125 problem 126

Internal problem ID [10139]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 126
Date solved : Monday, January 27, 2025 at 06:29:41 PM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} x y^{\prime }-y f \left (y x \right )&=0 \end{align*}

✓ Solution by Maple

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

dsolve(x*diff(y(x),x) - y(x)*f(x*y(x))=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.203 (sec). Leaf size: 115

DSolve[x*D[y[x],x] - y[x]*f[x*y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
 

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