Internal problem ID [4306]
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: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-16 y-40 \,{\mathrm e}^{4 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)-16*y(x)=40*exp(4*x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{4 x} c_{2}+{\mathrm e}^{-4 x} c_{1}+5 \,{\mathrm e}^{4 x} x \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 29
DSolve[y''[x]-16*y[x]==40*Exp[4*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{4 x} \left (5 x-\frac {5}{8}+c_1\right )+c_2 e^{-4 x} \\ \end{align*}