88.23.12 problem 14

Internal problem ID [24186]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 5. Special Techniques for Linear Equations. Miscellaneous Exercises at page 162
Problem number : 14
Date solved : Thursday, October 02, 2025 at 10:00:35 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 33

ode:=diff(diff(y(x),x),x)+I*y(x) = cosh(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sin \left (\left (\frac {1}{2}+\frac {i}{2}\right ) \sqrt {2}\, x \right ) c_2 +\cos \left (\left (\frac {1}{2}+\frac {i}{2}\right ) \sqrt {2}\, x \right ) c_1 +\left (\frac {1}{2}-\frac {i}{2}\right ) \cosh \left (x \right ) \]

✓ Mathematica. Time used: 0.101 (sec). Leaf size: 46

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

\begin{align*} y(x)&\to \left (\frac {1}{2}-\frac {i}{2}\right ) \cosh (x)+c_1 e^{\frac {(1-i) x}{\sqrt {2}}}+c_2 e^{-\frac {(1-i) x}{\sqrt {2}}} \end{align*}

✓ Sympy. Time used: 0.136 (sec). Leaf size: 37

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(I*y(x) - cosh(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (\frac {1}{2} + \frac {i}{2}\right ) \left (C_{1} e^{- x \sqrt {- i}} + C_{2} e^{x \sqrt {- i}} - i \cosh {\left (x \right )}\right ) \]