81.11.19 problem 15-18

Internal problem ID [21643]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 15. Method of undetermined coefficients. Page 337.
Problem number : 15-18
Date solved : Thursday, October 02, 2025 at 07:59:22 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 0.108 (sec). Leaf size: 15

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

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