80.3.20 problem 21

Internal problem ID [21184]
Book : A Textbook on Ordinary Differential Equations by Shair Ahmad and Antonio Ambrosetti. Second edition. ISBN 978-3-319-16407-6. Springer 2015
Section : Chapter 3. First order nonlinear differential equations. Excercise 3.7 at page 67
Problem number : 21
Date solved : Thursday, October 02, 2025 at 07:16:06 PM
CAS classification : [_exact, _rational]

\begin{align*} a \,x^{p}+b y+\left (b x +d y^{q}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.024 (sec). Leaf size: 35

ode:=a*x^p+b*y(x)+(b*x+d*y(x)^q)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {a \,x^{p +1}}{p +1}+b x y+\frac {d y^{q +1}}{q +1}+c_1 = 0 \]

✓ Mathematica. Time used: 0.281 (sec). Leaf size: 37

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

\[ \text {Solve}\left [\frac {a x^{p+1}}{p+1}+b x y(x)+\frac {d y(x)^{q+1}}{q+1}=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
p = symbols("p") 
b = symbols("b") 
d = symbols("d") 
q = symbols("q") 
y = Function("y") 
ode = Eq(a*x**p + b*y(x) + (b*x + d*y(x)**q)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out