60.1.538 problem 551

Internal problem ID [10552]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 551
Date solved : Sunday, March 30, 2025 at 06:00:16 PM
CAS classification : [_separable]

\begin{align*} {y^{\prime }}^{n}-f \left (x \right )^{n} \left (y-a \right )^{n +1} \left (y-b \right )^{n -1}&=0 \end{align*}

✓ Maple. Time used: 0.506 (sec). Leaf size: 55

ode:=diff(y(x),x)^n-f(x)^n*(y(x)-a)^(n+1)*(y(x)-b)^(n-1) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (-\frac {n}{\left (a -b \right ) \left (\int f \left (x \right )d x +c_1 \right )}\right )^{n} b -a}{-1+\left (-\frac {n}{\left (a -b \right ) \left (\int f \left (x \right )d x +c_1 \right )}\right )^{n}} \]

✓ Mathematica. Time used: 23.971 (sec). Leaf size: 79

ode=-(f[x]^n*(-a + y[x])^(1 + n)*(-b + y[x])^(-1 + n)) + D[y[x],x]^n==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {b n^n+a (a-b)^n \left (\int _1^x-(-1)^{\frac {1}{n}} f(K[1])dK[1]+c_1\right ){}^n}{n^n+(a-b)^n \left (\int _1^x-(-1)^{\frac {1}{n}} f(K[1])dK[1]+c_1\right ){}^n} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
n = symbols("n") 
y = Function("y") 
f = Function("f") 
ode = Eq(-(-a + y(x))**(n + 1)*(-b + y(x))**(n - 1)*f(x)**n + Derivative(y(x), x)**n,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out