14.12.13 problem Problem 32

Internal problem ID [3807]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.10, Chapter review. page 575
Problem number : Problem 32
Date solved : Tuesday, September 30, 2025 at 06:57:35 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=5 \,{\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 28

ode:=diff(diff(y(x),x),x)+2*diff(y(x),x)-3*y(x) = 5*exp(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (5 x +4 c_2 \right ) {\mathrm e}^{-3 x} {\mathrm e}^{4 x}}{4}+{\mathrm e}^{-3 x} c_1 \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 29

ode=D[y[x],{x,2}]+2*D[y[x],x]-3*y[x]==5*Exp[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{-3 x}+e^x \left (\frac {5 x}{4}-\frac {5}{16}+c_2\right ) \end{align*}

✓ Sympy. Time used: 0.130 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*y(x) - 5*exp(x) + 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{2} e^{- 3 x} + \left (C_{1} + \frac {5 x}{4}\right ) e^{x} \]