23.1.8 problem 7

Internal problem ID [4615]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 7
Date solved : Tuesday, September 30, 2025 at 07:37:02 AM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 30

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

\[ y = \frac {b \,{\mathrm e}^{k x}}{-c +k}-\frac {a}{c}+{\mathrm e}^{c x} c_1 \]

✓ Mathematica. Time used: 0.147 (sec). Leaf size: 47

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

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

✓ Sympy. Time used: 0.089 (sec). Leaf size: 22

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

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