23.1.747 problem 750

Internal problem ID [5354]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 750
Date solved : Tuesday, September 30, 2025 at 12:35:21 PM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.060 (sec). Leaf size: 180

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

\[ y = -\frac {{\mathrm e}^{-\operatorname {RootOf}\left (\textit {\_Z} \,{\mathrm e}^{\textit {\_Z} +2 x}-x \,{\mathrm e}^{\textit {\_Z} +2 x}+x \,{\mathrm e}^{2 \textit {\_Z}}+2 c_1 \,{\mathrm e}^{\textit {\_Z} +x}-x \,{\mathrm e}^{2 x}-\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+x \,{\mathrm e}^{\textit {\_Z}}\right )} \left (2 c_1 \,{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z} \,{\mathrm e}^{\textit {\_Z} +2 x}-x \,{\mathrm e}^{\textit {\_Z} +2 x}+x \,{\mathrm e}^{2 \textit {\_Z}}+2 c_1 \,{\mathrm e}^{\textit {\_Z} +x}-x \,{\mathrm e}^{2 x}-\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+x \,{\mathrm e}^{\textit {\_Z}}\right )+x}+x \left ({\mathrm e}^{2 \operatorname {RootOf}\left (\textit {\_Z} \,{\mathrm e}^{\textit {\_Z} +2 x}-x \,{\mathrm e}^{\textit {\_Z} +2 x}+x \,{\mathrm e}^{2 \textit {\_Z}}+2 c_1 \,{\mathrm e}^{\textit {\_Z} +x}-x \,{\mathrm e}^{2 x}-\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+x \,{\mathrm e}^{\textit {\_Z}}\right )}-{\mathrm e}^{2 x}\right )\right )}{{\mathrm e}^{2 x}-1} \]

✓ Mathematica. Time used: 0.171 (sec). Leaf size: 56

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

\[ \text {Solve}\left [\int _1^x(\sinh (y(x))+\cosh (K[1]) y(x))dK[1]+\int _1^{y(x)}\left (x \cosh (K[2])+\sinh (x)-\int _1^x(\cosh (K[1])+\cosh (K[2]))dK[1]\right )dK[2]=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out