89.23.14 problem 14

Internal problem ID [24818]
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. Miscellaneous Exercises at page 162
Problem number : 14
Date solved : Thursday, October 02, 2025 at 10:48:17 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} 4 y+y^{\prime \prime }&=20 \,{\mathrm e}^{x}-20 \cos \left (2 x \right ) \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 25

ode:=diff(diff(y(x),x),x)+4*y(x) = 20*exp(x)-20*cos(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_2 -5 x \right ) \sin \left (2 x \right )+\cos \left (2 x \right ) c_1 +4 \,{\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.326 (sec). Leaf size: 33

ode=D[y[x],{x,2}]+4*y[x]==20*(Exp[x]-Cos[2*x]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 4 e^x+\left (-\frac {5}{4}+c_1\right ) \cos (2 x)+(-5 x+c_2) \sin (2 x) \end{align*}

✓ Sympy. Time used: 0.059 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*y(x) - 20*exp(x) + 20*cos(2*x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{2} \cos {\left (2 x \right )} + \left (C_{1} - 5 x\right ) \sin {\left (2 x \right )} + 4 e^{x} \]