74.2.14 problem 19

Internal problem ID [15776]
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 : Thursday, March 13, 2025 at 06:19:37 AM
CAS classification : [_quadrature]

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

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

ode:=diff(y(x),x) = x^2/(x^2-1)^(1/2); 
dsolve(ode,y(x), singsol=all);
 

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

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

ode=D[y[x],x]==x^2/Sqrt[x^2-1]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.222 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2/sqrt(x**2 - 1) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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