15.7.3 problem 3

Internal problem ID [2984]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 11, page 45
Problem number : 3
Date solved : Sunday, March 30, 2025 at 01:03:29 AM
CAS classification : [`y=_G(x,y')`]

\begin{align*} \cosh \left (y\right ) y^{\prime }+\sinh \left (y\right )-{\mathrm e}^{-x}&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 17

ode:=cosh(y(x))*diff(y(x),x)+sinh(y(x))-exp(-x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\operatorname {arcsinh}\left (\left (-x +c_1 \right ) {\mathrm e}^{-x}\right ) \]

✓ Mathematica. Time used: 13.947 (sec). Leaf size: 16

ode=Cosh[y[x]]*D[y[x],x]+(Sinh[y[x]]-Exp[-x] )==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \text {arcsinh}\left (e^{-x} (x+c_1)\right ) \]

✓ Sympy. Time used: 2.253 (sec). Leaf size: 61

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

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