79.6.3 problem (c)

Internal problem ID [21099]
Book : Ordinary Differential Equations. By Wolfgang Walter. Graduate texts in Mathematics. Springer. NY. QA372.W224 1998
Section : Chapter 1. First order equations: Some integrable cases. Excercises VIII at page 51
Problem number : (c)
Date solved : Thursday, October 02, 2025 at 07:08:15 PM
CAS classification : [_separable]

\begin{align*} y&=x y^{\prime }+a y^{\prime }+b \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 11

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

\[ y = \left (a +x \right ) c_1 +b \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 18

ode=y[x]==x*D[y[x],x]+a*D[y[x],x]+b; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to b+c_1 (a+x)\\ y(x)&\to b \end{align*}

✓ Sympy. Time used: 0.153 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = C_{1} a + C_{1} x + b \]