84.24.3 problem 14.12

Internal problem ID [22256]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 14. The method of undetermined coefficients. Supplementary problems
Problem number : 14.12
Date solved : Thursday, October 02, 2025 at 08:36:43 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=4 \cos \left (x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

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

\[ y = \left (c_1 x +c_2 \right ) {\mathrm e}^{x}-2 \sin \left (x \right ) \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 21

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

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

✓ Sympy. Time used: 0.121 (sec). Leaf size: 15

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

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