15.12.2 problem 2

Internal problem ID [3146]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 20, page 90
Problem number : 2
Date solved : Monday, January 27, 2025 at 07:23:37 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

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

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

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 26

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

\[ y(x)\to \frac {e^x}{9}+e^{-2 x} (c_2 x+c_1) \]