74.2.14 problem 19

Internal problem ID [15855]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Review exercises, page 23
Problem number : 19
Date solved : Tuesday, January 28, 2025 at 08:10:21 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 28

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

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

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 36

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

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