Internal problem ID [4293]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 5. SECOND-ORDER LINEAR
EQUATIONSWITH CONSTANT COEFFICIENTS AND ZERO RIGHT-HAND SIDE. page
414
Problem number: 19.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\left (1+2 i\right ) y^{\prime }+\left (-1+i\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(diff(y(x),x$2)+(1+2*I)*diff(y(x),x)+(I-1)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{\left (-1-i\right ) x}+c_{2} {\mathrm e}^{-i x} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 22
DSolve[y''[x]+(1+2*I)*y'[x]+(I-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{(-1-i) x} \left (c_2 e^x+c_1\right ) \\ \end{align*}