Internal problem ID [5204]
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(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+\left (1+4 i\right ) y^{\prime }+y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 5
dsolve([diff(y(x),x$2)+(4*I+1)*diff(y(x),x)+y(x)=0,y(0) = 0, D(y)(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = 0 \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 6
DSolve[{y''[x]+(4*I+1)*y'[x]+y[x]==0,{y[0]==0,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 0 \\ \end{align*}