Internal problem ID [14118]
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: 18.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }=\frac {2 x^{2}-x +1}{\left (x -1\right ) \left (x^{2}+1\right )}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(diff(y(x),x)=(2*x^2-x+1)/( (x-1)*(x^2+1)),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\ln \left (x^{2}+1\right )}{2}+\ln \left (-1+x \right )+c_{1} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 24
DSolve[y'[x]==(2*x^2-x+1)/( (x-1)*(x^2+1)),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \log \left (x^2+1\right )+\log (1-x)+c_1 \]