49.6.9 problem 1(i)

Internal problem ID [7637]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 69
Problem number : 1(i)
Date solved : Monday, January 27, 2025 at 03:08:46 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 21

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

\[ y = c_{2} {\mathrm e}^{\frac {x}{2}}+{\mathrm e}^{-\frac {x}{2}} c_{1} +\frac {{\mathrm e}^{x}}{3} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 33

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

\[ y(x)\to \frac {e^x}{3}+c_1 e^{x/2}+c_2 e^{-x/2} \]