60.1.125 problem 128

Internal problem ID [10139]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 128
Date solved : Sunday, March 30, 2025 at 03:19:37 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

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

✓ Maple. Time used: 0.053 (sec). Leaf size: 33

ode:=x*diff(y(x),x)+a*y(x)-f(x)*g(x^a*y(x)) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \operatorname {RootOf}\left (-\int f \left (x \right ) x^{a -1}d x +\int _{}^{\textit {\_Z}}\frac {1}{g \left (\textit {\_a} \right )}d \textit {\_a} +c_1 \right ) x^{-a} \]

✓ Mathematica. Time used: 0.552 (sec). Leaf size: 41

ode=x*D[y[x],x] + a*y[x] - f[x]*g[x^a*y[x]]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(a*y(x) + x*Derivative(y(x), x) - f(x)*g(x**a*y(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out