89.21.5 problem 7

Internal problem ID [24777]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 10. Nonhomogeneous Equations: Operational methods. Exercises at page 154
Problem number : 7
Date solved : Thursday, October 02, 2025 at 10:47:55 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

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

\[ y = {\mathrm e}^{x} \left (\left (c_1 +x -1\right ) {\mathrm e}^{x}+c_2 -x \right ) \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 25

ode=D[y[x],{x,2}]-3*D[y[x],{x,1}]+2*y[x]== Exp[x]+Exp[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^x \left (-x+e^x (x-1+c_2)-1+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.141 (sec). Leaf size: 15

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

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