60.1.51 problem 52

Internal problem ID [10065]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 52
Date solved : Sunday, March 30, 2025 at 02:59:35 PM
CAS classification : [[_homogeneous, `class G`], _Chini]

\begin{align*} y^{\prime }-a y^{n}-b \,x^{\frac {n}{1-n}}&=0 \end{align*}

✓ Maple. Time used: 0.109 (sec). Leaf size: 65

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

\[ x^{\frac {n}{-1+n}} \int _{\textit {\_b}}^{y}\frac {1}{a \,\textit {\_a}^{n} \left (-1+n \right ) x^{\frac {-1+2 n}{-1+n}}+x^{\frac {n}{-1+n}} \textit {\_a} +b x \left (-1+n \right )}d \textit {\_a} -c_1 = 0 \]

✓ Mathematica. Time used: 1.297 (sec). Leaf size: 117

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

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

✗ Sympy

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

NotImplementedError : The given ODE -a*y(x)**n - b/x**(n/(n - 1)) + Derivative(y(x), x) cannot be solved by the factorable group method