Internal problem ID [4423]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page
46
Problem number: 20.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}-\frac {4 x^{2}-x -2}{\left (x +1\right ) \left (1+y\right )}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.266 (sec). Leaf size: 38
dsolve([x^2*diff(y(x),x)=(4*x^2-x-2)/((x+1)*(y(x)+1)),y(1) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {-x +\sqrt {2}\, \sqrt {x \left (\ln \relax (x ) x +3 \ln \left (x +1\right ) x -3 \ln \relax (2) x +2\right )}}{x} \]
✓ Solution by Mathematica
Time used: 0.435 (sec). Leaf size: 36
DSolve[{x^2*y'[x]==(4*x^2-x-2)/((x+1)*(y[x]+1)),{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt {2 x \log (x)+6 x \log (x+1)-6 x \log (2)+4}}{\sqrt {x}}-1 \\ \end{align*}