Internal problem ID [4301]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR
EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page
422
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y^{\prime }-2 y-{\mathrm e}^{2 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 21
dsolve(diff(y(x),x$2)+diff(y(x),x)-2*y(x)=exp(2*x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{x}+{\mathrm e}^{-2 x} c_{1}+\frac {{\mathrm e}^{2 x}}{4} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 29
DSolve[y''[x]+y'[x]-2*y[x]==Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{2 x}}{4}+c_1 e^{-2 x}+c_2 e^x \\ \end{align*}