88.23.2 problem 2

Internal problem ID [24176]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 5. Special Techniques for Linear Equations. Miscellaneous Exercises at page 162
Problem number : 2
Date solved : Thursday, October 02, 2025 at 10:00:27 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \cos \left (x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 20

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

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

✓ Sympy. Time used: 0.136 (sec). Leaf size: 14

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

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