60.1.202 problem 206

Internal problem ID [10216]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 206
Date solved : Wednesday, March 05, 2025 at 08:43:52 AM
CAS classification : [[_Abel, `2nd type`, `class A`]]

\begin{align*} y y^{\prime }+a y+b \,{\mathrm e}^{x}-2 a&=0 \end{align*}

✗ Maple

ode:=y(x)*diff(y(x),x)+a*y(x)+b*exp(x)-2*a = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=y[x]*D[y[x],x]+a*y[x]+b*Exp[x]-2*a==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") 
y = Function("y") 
ode = Eq(a*y(x) - 2*a + b*exp(x) + y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -(-a*y(x) + 2*a - b*exp(x))/y(x) + Derivative(y(x), x) cannot be solved by the factorable group method