60.1.201 problem 205

Internal problem ID [10215]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 205
Date solved : Sunday, March 30, 2025 at 03:31:56 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y y^{\prime }+a y+\frac {\left (a^{2}-1\right ) x}{4}+b \,x^{n}&=0 \end{align*}

✗ Maple

ode:=y(x)*diff(y(x),x)+a*y(x)+1/4*(a^2-1)*x+b*x^n = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]+a*y[x]+(a^2-1)/(4)*x+b*x^n==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
n = symbols("n") 
y = Function("y") 
ode = Eq(a*y(x) + b*x**n + x*(a**2 - 1)/4 + y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out