Internal problem ID [5381]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (1+x \right ) \left (x^{2}+1\right ) y^{\prime }-2 x^{2}-x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.01 (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)
\[ y \relax (x ) = \frac {3 \ln \left (x^{2}+1\right )}{4}-\frac {\arctan \relax (x )}{2}+\frac {\ln \left (x +1\right )}{2}+1 \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 29
DSolve[{(x+1)*(x^2+1)*y'[x]==2*x^2+x,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (-2 \text {ArcTan}(x)+3 \log \left (x^2+1\right )+2 \log (x+1)+4\right ) \\ \end{align*}