Internal problem ID [5250]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 2. Linear equations with constant coefficients. Page 93
Problem number: 1(g).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+i y^{\prime }+2 y-2 \cosh \left (2 x \right )-{\mathrm e}^{-2 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.045 (sec). Leaf size: 35
dsolve(diff(y(x),x$2)+I*diff(y(x),x)+2*y(x)=2*cosh(2*x)+exp(-2*x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{i x}+{\mathrm e}^{-2 i x} c_{1}+\left (\frac {3}{10}+\frac {i}{10}\right ) {\mathrm e}^{-2 x}+\left (\frac {3}{20}-\frac {i}{20}\right ) {\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.067 (sec). Leaf size: 47
DSolve[y''[x]+I*y'[x]+2*y[x]==2*Cosh[2*x]+Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-2 i x}+c_2 e^{i x}+\frac {1}{20} ((9+i) \cosh (2 x)-(3+3 i) \sinh (2 x)) \\ \end{align*}