73.3.4 problem 4.3 (d)

Internal problem ID [15038]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.3 (d)
Date solved : Tuesday, January 28, 2025 at 07:28:15 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 20

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

\[ y = \frac {x \sqrt {x^{2}+1}}{2}+\frac {\operatorname {arcsinh}\left (x \right )}{2}+c_{1} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 26

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

\[ y(x)\to \frac {1}{2} \left (\text {arcsinh}(x)+\sqrt {x^2+1} x\right )+c_1 \]