50.1.30 problem 3(f)

Internal problem ID [7802]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.2 THE NATURE OF SOLUTIONS. Page 9
Problem number : 3(f)
Date solved : Monday, January 27, 2025 at 03:23:28 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 24

dsolve([(x+1)*(x^2+1)*diff(y(x),x)=2*x^2+x,y(0) = 1],y(x), singsol=all)
 

\[ y = \frac {\ln \left (x +1\right )}{2}+\frac {3 \ln \left (x^{2}+1\right )}{4}-\frac {\arctan \left (x \right )}{2}+1 \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 29

DSolve[{(x+1)*(x^2+1)*D[y[x],x]==2*x^2+x,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} \left (-2 \arctan (x)+3 \log \left (x^2+1\right )+2 \log (x+1)+4\right ) \]