Internal problem ID [5216]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {4 y^{\prime \prime }-y-{\mathrm e}^{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(4*diff(y(x),x$2)-y(x)=exp(x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\frac {x}{2}} c_{2}+{\mathrm e}^{\frac {x}{2}} c_{1}+\frac {{\mathrm e}^{x}}{3} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 33
DSolve[4*y''[x]-y[x]==Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^x}{3}+c_1 e^{x/2}+c_2 e^{-x/2} \\ \end{align*}