77.1.41 problem 58 (page 103)

Internal problem ID [17860]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 58 (page 103)
Date solved : Monday, March 31, 2025 at 04:37:21 PM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} a x y^{\prime }+b y+x^{m} y^{n} \left (\alpha x y^{\prime }+\beta y\right )&=0 \end{align*}

✓ Maple. Time used: 0.170 (sec). Leaf size: 71

ode:=a*x*diff(y(x),x)+b*y(x)+x^m*y(x)^n*(alpha*x*diff(y(x),x)+beta*y(x)) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \left (x^{m} \left (\alpha m -\beta n \right ) y^{n}+a m -b n \right )^{n \left (a \beta -\alpha b \right )} x^{b n \left (\alpha m -\beta n \right )} \left (y^{n}\right )^{a \left (\alpha m -\beta n \right )}-c_1 = 0 \]

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 46

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

\begin{align*} y(x)\to \left (-x^{-m}\right )^{\frac {1}{n}} \\ y(x)\to c_1 x^{-\frac {b}{a}} \\ y(x)\to \left (-x^{-m}\right )^{\frac {1}{n}} \\ \end{align*}

✗ Sympy

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

Timed Out