15.14.2 problem 2

Internal problem ID [3174]
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 : 2
Date solved : Monday, January 27, 2025 at 07:24:59 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

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

\[ y = \sin \left (\sqrt {3}\, x \right ) c_2 +\cos \left (\sqrt {3}\, x \right ) c_{1} +\frac {3 \,{\mathrm e}^{-4 x}}{19} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 37

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

\[ y(x)\to \frac {3 e^{-4 x}}{19}+c_1 \cos \left (\sqrt {3} x\right )+c_2 \sin \left (\sqrt {3} x\right ) \]