Internal problem ID [209]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.3, second order linear equations. Page 323
Problem number: 47.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-\left (-2+2 i \sqrt {3}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 31
dsolve(diff(y(x),x$2)=(-2+2*I*sqrt(3))*y(x),y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{\left (1+i \sqrt {3}\right ) x}+c_{2} {\mathrm e}^{\left (-i \sqrt {3}-1\right ) x} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 41
DSolve[y''[x]==(-2+2*I*Sqrt[3])*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{x+i \sqrt {3} x}+c_2 e^{\left (-1-i \sqrt {3}\right ) x} \\ \end{align*}