81.14.16 problem 18-29

Internal problem ID [21701]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 18. Algebra of differential operators. Page 435
Problem number : 18-29
Date solved : Thursday, October 02, 2025 at 08:00:08 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&={\mathrm e}^{2 x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

ode:=diff(diff(y(x),x),x)+4*diff(y(x),x)+3*y(x) = exp(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-3 x} c_2 +{\mathrm e}^{-x} c_1 +\frac {{\mathrm e}^{2 x}}{15} \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 31

ode=D[y[x],{x,2}]+4*D[y[x],x]+3*y[x]==Exp[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {e^{2 x}}{15}+c_1 e^{-3 x}+c_2 e^{-x} \end{align*}

✓ Sympy. Time used: 0.116 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*y(x) - exp(2*x) + 4*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 3 x} + C_{2} e^{- x} + \frac {e^{2 x}}{15} \]