44.1.5 problem 5

Internal problem ID [6880]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Exercises 1.1 at page 12
Problem number : 5
Date solved : Monday, January 27, 2025 at 02:32:12 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.201 (sec). Leaf size: 26

dsolve(diff(y(x),x$2)=sqrt(1+diff(y(x),x)^2),y(x), singsol=all)
 

\begin{align*} y &= -i x +c_{1} \\ y &= i x +c_{1} \\ y &= \cosh \left (x +c_{1} \right )+c_{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.294 (sec). Leaf size: 13

DSolve[D[y[x],{x,2}]==Sqrt[1+D[y[x],x]^2],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \cosh (x+c_1)+c_2 \]