15.14.3 problem 3

Internal problem ID [3175]
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 : 3
Date solved : Monday, January 27, 2025 at 07:25:03 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 26

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

\[ y = \frac {\left ({\mathrm e}^{3 x}+18 c_{1} x +9 \,{\mathrm e}^{x}+18 c_2 \right ) {\mathrm e}^{-2 x}}{18} \]

✓ Solution by Mathematica

Time used: 0.287 (sec). Leaf size: 34

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

\[ y(x)\to \frac {1}{18} e^{-2 x} \left (9 e^x+e^{3 x}+18 (c_2 x+c_1)\right ) \]