Internal problem ID [4074]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 20. Constant coefficients
Problem number: Exercise 20.12, page 220.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 k y^{\prime }-12 k^{2} y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(y(x),x$2)+4*k*diff(y(x),x)-12*k^2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{2 k x}+c_{2} {\mathrm e}^{-6 k x} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 24
DSolve[y''[x]+4*k*y'[x]-12*k^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-6 k x} \left (c_2 e^{8 k x}+c_1\right ) \\ \end{align*}