74.1.34 problem 41

Internal problem ID [15814]
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
Date solved : Tuesday, January 28, 2025 at 08:08:04 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\frac {-x^{2}+x}{\left (1+x \right ) \left (x^{2}+1\right )} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

dsolve(diff(y(x),x)=(x-x^2)/((x+1)*(x^2+1)),y(x), singsol=all)
 

\[ y = -\ln \left (x +1\right )+\arctan \left (x \right )+c_{1} \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 37

DSolve[D[y[x],x]==(x-x^2)/((x+1)*(x^2+1)),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^x-\frac {(K[1]-1) K[1]}{K[1]^3+K[1]^2+K[1]+1}dK[1]+c_1 \]