89.10.6 problem 6

Internal problem ID [24499]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 4. Additional topics on equations of first order and first degree. Exercises at page 77
Problem number : 6
Date solved : Thursday, October 02, 2025 at 10:43:09 PM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 31

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

\[ y = \frac {{\mathrm e}^{b x} c_1 \,b^{2}+\left (-a x -c \right ) b -a}{b^{2}} \]

✓ Mathematica. Time used: 0.066 (sec). Leaf size: 28

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

\begin{align*} y(x)&\to -\frac {a b x+a+b c}{b^2}+c_1 e^{b x} \end{align*}

✓ Sympy. Time used: 0.082 (sec). Leaf size: 22

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

\[ y{\left (x \right )} = C_{1} e^{b x} - \frac {a x}{b} - \frac {a}{b^{2}} - \frac {c}{b} \]