15.14.6 problem 6

Internal problem ID [3178]
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 : 6
Date solved : Monday, January 27, 2025 at 07:25:11 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {{\mathrm e}^{3 x}}{2}-\frac {{\mathrm e}^{-3 x}}{2} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 25

dsolve(diff(y(x),x$2)+4*diff(y(x),x)+4*y(x)=1/2*(exp(3*x)-exp(-3*x)),y(x), singsol=all)
 

\[ y = \frac {\left (-25+{\mathrm e}^{6 x}+50 \left (c_{1} x +c_2 \right ) {\mathrm e}^{x}\right ) {\mathrm e}^{-3 x}}{50} \]

✓ Solution by Mathematica

Time used: 0.225 (sec). Leaf size: 33

DSolve[D[y[x],{x,2}]+4*D[y[x],x]+4*y[x]==1/2*(Exp[3*x]-Exp[-3*x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{50} e^{-3 x} \left (e^{6 x}+50 e^x (c_2 x+c_1)-25\right ) \]