44.5.73 problem 62 (a)

Internal problem ID [7135]
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 : 62 (a)
Date solved : Tuesday, February 04, 2025 at 12:33:12 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.043 (sec). Leaf size: 8

dsolve([diff(u(x),x)= a*sqrt(1+u(x)^2),u(0) = 0],u(x), singsol=all)
 

\[ u = \sinh \left (x a \right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 9

DSolve[{D[u[x],x]== a*Sqrt[1+u[x]^2],{u[0]==0}},u[x],x,IncludeSingularSolutions -> True]
 

\[ u(x)\to \sinh (a x) \]