35.6.29 problem 35

Internal problem ID [6179]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page 422
Problem number : 35
Date solved : Sunday, March 30, 2025 at 10:42:08 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-y&=\sinh \left (x \right ) \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 28

ode:=diff(diff(y(x),x),x)-y(x) = sinh(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{-x} \left (8 c_2 +2 x \right )}{8}+\frac {{\mathrm e}^{x} \left (x +4 c_1 -\frac {1}{2}\right )}{4} \]

✓ Mathematica. Time used: 0.049 (sec). Leaf size: 38

ode=D[y[x],{x,2}]-y[x]==Sinh[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{8} e^{-x} \left (2 x+e^{2 x} (2 x-1+8 c_1)+1+8 c_2\right ) \]

✓ Sympy. Time used: 0.094 (sec). Leaf size: 19

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

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