Internal problem ID [5206]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 2. Linear equations with constant coefficients. Page 59
Problem number: 1(c).
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+3 i\right ) y^{\prime }-3 i y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 20
dsolve([diff(y(x),x$2)+(3*I-1)*diff(y(x),x)-3*I*y(x)=0,y(0) = 2, D(y)(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = \left (\frac {9}{5}+\frac {3 i}{5}\right ) {\mathrm e}^{x}+\left (\frac {1}{5}-\frac {3 i}{5}\right ) {\mathrm e}^{-3 i x} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 31
DSolve[{y''[x]+(3*I-1)*y'[x]-3*I*y[x]==0,{y[0]==2,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{5} e^{-3 i x} \left ((9+3 i) e^{(1+3 i) x}+(1-3 i)\right ) \\ \end{align*}