15.11.1 problem 1

Internal problem ID [3111]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 19, page 86
Problem number : 1
Date solved : Tuesday, March 04, 2025 at 03:58:45 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y&=3 \cos \left (x \right ) \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 21

ode:=diff(diff(y(x),x),x)-4*y(x) = 3*cos(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_2 \,{\mathrm e}^{-2 x}+c_{1} {\mathrm e}^{2 x}-\frac {3 \cos \left (x \right )}{5} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 28

ode=D[y[x],{x,2}]-4*y[x]==3*Cos[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {3 \cos (x)}{5}+c_1 e^{2 x}+c_2 e^{-2 x} \]

✓ Sympy. Time used: 0.073 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*y(x) - 3*cos(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 2 x} + C_{2} e^{2 x} - \frac {3 \cos {\left (x \right )}}{5} \]