15.14.14 problem 14

Internal problem ID [3186]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 23, page 106
Problem number : 14
Date solved : Monday, January 27, 2025 at 07:25:25 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+5 y&=\frac {{\mathrm e}^{x}}{2}+\frac {{\mathrm e}^{-x}}{2} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 29

dsolve(diff(y(x),x$2)+4*diff(y(x),x)+5*y(x)=1/2*(exp(x)+exp(-x)),y(x), singsol=all)
 

\[ y = \frac {\left ({\mathrm e}^{3 x}+20 c_2 \sin \left (x \right )+20 \cos \left (x \right ) c_{1} +5 \,{\mathrm e}^{x}\right ) {\mathrm e}^{-2 x}}{20} \]

✓ Solution by Mathematica

Time used: 0.245 (sec). Leaf size: 37

DSolve[D[y[x],{x,2}]+4*D[y[x],x]+5*y[x]==1/2*(Exp[x]+Exp[-x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{20} e^{-2 x} \left (5 e^x+e^{3 x}+20 c_2 \cos (x)+20 c_1 \sin (x)\right ) \]