Internal problem ID [13799]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }=\frac {x^{2}}{\sqrt {x^{2}-1}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(diff(y(x),x)=x^2/sqrt(x^2-1),y(x), singsol=all)
\[ y \left (x \right ) = \frac {x \sqrt {x^{2}-1}}{2}+\frac {\ln \left (x +\sqrt {x^{2}-1}\right )}{2}+c_{1} \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 40
DSolve[y'[x]==x^2/Sqrt[x^2-1],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \sqrt {x^2-1} x-\frac {1}{2} \log \left (\sqrt {x^2-1}-x\right )+c_1 \]