23.3.70 problem 72

Internal problem ID [5784]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 72
Date solved : Tuesday, September 30, 2025 at 02:03:01 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=8 \sinh \left (x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 36

ode:=5*y(x)+2*diff(y(x),x)+diff(diff(y(x),x),x) = 8*sinh(x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.06 (sec). Leaf size: 37

ode=5*y[x] + 2*D[y[x],x] + D[y[x],{x,2}] == 8*Sinh[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.180 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*y(x) - 8*sinh(x) + 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} \sin {\left (2 x \right )} + C_{2} \cos {\left (2 x \right )}\right ) e^{- x} + \frac {3 \sinh {\left (x \right )}}{2} - \frac {\cosh {\left (x \right )}}{2} \]