Internal problem ID [14078]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number: 41.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }=\frac {-x^{2}+x}{\left (x +1\right ) \left (x^{2}+1\right )}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(diff(y(x),x)=(x-x^2)/((x+1)*(x^2+1)),y(x), singsol=all)
\[ y \left (x \right ) = -\ln \left (1+x \right )+\arctan \left (x \right )+c_{1} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 16
DSolve[y'[x]==(x-x^2)/((x+1)*(x^2+1)),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \arctan (x)-\log (x+1)+c_1 \]