49.11.7 problem 1(g)

Internal problem ID [7671]
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)
Date solved : Monday, January 27, 2025 at 03:09:33 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+i y^{\prime }+2 y&=2 \cosh \left (2 x \right )+{\mathrm e}^{-2 x} \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 29

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)
 

\[ y = c_{2} {\mathrm e}^{i x}+c_{1} {\mathrm e}^{-2 i x}+\left (\frac {3}{10}+\frac {i}{10}\right ) {\mathrm e}^{-2 x}+\left (\frac {3}{20}-\frac {i}{20}\right ) {\mathrm e}^{2 x} \]

✓ Solution by Mathematica

Time used: 0.227 (sec). Leaf size: 48

DSolve[D[y[x],{x,2}]+I*D[y[x],x]+2*y[x]==2*Cosh[2*x]+Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{20} e^{-2 x} \left ((3-i) e^{4 x}+(6+2 i)\right )+c_1 e^{-2 i x}+c_2 e^{i x} \]