Internal problem ID [14241]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-\frac {x y}{x^{2}-1}=2 x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x)=2*x+x*y(x)/(x^2-1),y(x), singsol=all)
\[ y \left (x \right ) = 2 x^{2}-2+\sqrt {-1+x}\, \sqrt {1+x}\, c_{1} \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 24
DSolve[y'[x]==2*x+x*y[x]/(x^2-1),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 2 x^2+c_1 \sqrt {x^2-1}-2 \]