30.2.7 problem 7

Internal problem ID [7435]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.3, Linear equations. Exercises. page 54
Problem number : 7
Date solved : Tuesday, September 30, 2025 at 04:35:18 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-y-{\mathrm e}^{3 x}&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

ode:=diff(y(x),x)-y(x)-exp(3*x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{3 x}}{2}+{\mathrm e}^{x} c_1 \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 21

ode=D[y[x],x]-y[x]-Exp[3*x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {e^{3 x}}{2}+c_1 e^x \end{align*}

✓ Sympy. Time used: 0.078 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x) - exp(3*x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + \frac {e^{2 x}}{2}\right ) e^{x} \]