74.2.13 problem 18

Internal problem ID [15854]
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
Date solved : Tuesday, January 28, 2025 at 08:10:20 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 18

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

\[ y = \frac {\ln \left (x^{2}+1\right )}{2}+\ln \left (x -1\right )+c_{1} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 44

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

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