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 : Monday, January 27, 2025 at 07:19:32 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

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

dsolve(diff(y(x),x$2)-4*y(x)=3*cos(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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