44.5.30 problem 30

Internal problem ID [7092]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 30
Date solved : Tuesday, January 28, 2025 at 08:48:52 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.494 (sec). Leaf size: 48

dsolve([x*sinh(y(x))*diff(y(x),x)=cosh(y(x)),y(1) = 0],y(x), singsol=all)
 

\begin{align*} y &= \operatorname {arccoth}\left (\frac {\sqrt {x^{4}-x^{2}}}{x^{2}-1}\right ) \\ y &= \operatorname {arccoth}\left (-\frac {\sqrt {x^{4}-x^{2}}}{x^{2}-1}\right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.878 (sec). Leaf size: 15

DSolve[{x*Sinh[y[x]]*D[y[x],x]==Cosh[y[x]],{y[1]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\text {arccosh}(x) \\ y(x)\to \text {arccosh}(x) \\ \end{align*}