29.25.23 problem 720

Internal problem ID [5310]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 25
Problem number : 720
Date solved : Friday, March 14, 2025 at 01:29:52 AM
CAS classification : [_Bernoulli]

\begin{align*} f \left (x \right ) y^{m} y^{\prime }+g \left (x \right ) y^{m +1}+h \left (x \right ) y^{n}&=0 \end{align*}

✓ Maple. Time used: 0.118 (sec). Leaf size: 61

ode:=f(x)*y(x)^m*diff(y(x),x)+g(x)*y(x)^(m+1)+h(x)*y(x)^n = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = {\mathrm e}^{-\int \frac {g \left (x \right )}{f \left (x \right )}d x} {\left (\left (n -m -1\right ) \left (\int \frac {h \left (x \right ) {\mathrm e}^{\left (-n +m +1\right ) \left (\int \frac {g \left (x \right )}{f \left (x \right )}d x \right )}}{f \left (x \right )}d x \right )+c_{1} \right )}^{\frac {1}{-n +m +1}} \]

✓ Mathematica. Time used: 12.49 (sec). Leaf size: 187

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

\begin{align*} y(x)\to \left (\exp \left ((m-n+1) \int _1^x-\frac {g(K[1])}{f(K[1])}dK[1]\right ) \left ((m-n+1) \int _1^x-\frac {\exp \left (-\left ((m-n+1) \int _1^{K[2]}-\frac {g(K[1])}{f(K[1])}dK[1]\right )\right ) h(K[2])}{f(K[2])}dK[2]+c_1\right )\right ){}^{\frac {1}{m-n+1}} \\ y(x)\to \left ((m-n+1) \exp \left ((m-n+1) \int _1^x-\frac {g(K[1])}{f(K[1])}dK[1]\right ) \int _1^x-\frac {\exp \left (-\left ((m-n+1) \int _1^{K[2]}-\frac {g(K[1])}{f(K[1])}dK[1]\right )\right ) h(K[2])}{f(K[2])}dK[2]\right ){}^{\frac {1}{m-n+1}} \\ \end{align*}

✗ Sympy

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

Timed Out