49.5.3 problem 1(c)

Internal problem ID [7627]
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)
Date solved : Monday, January 27, 2025 at 03:08:02 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+\left (-1+3 i\right ) y^{\prime }-3 i y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 15

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)
 

\[ y = \left (\frac {1}{5}-\frac {3 i}{5}\right ) {\mathrm e}^{-3 i x}+\left (\frac {9}{5}+\frac {3 i}{5}\right ) {\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 31

DSolve[{D[y[x],{x,2}]+(3*I-1)*D[y[x],x]-3*I*y[x]==0,{y[0]==2,Derivative[1][y][0] ==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{5} e^{-3 i x} \left ((9+3 i) e^{(1+3 i) x}+(1-3 i)\right ) \]