Internal problem ID [4931]
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]
\[ \boxed {x^{2} y^{\prime }-\frac {4 x^{2}-x -2}{\left (x +1\right ) \left (1+y\right )}=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.125 (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)
\[ y \left (x \right ) = \frac {-x +\sqrt {2}\, \sqrt {x \left (\ln \left (x \right ) x -3 \ln \left (2\right ) x +3 \ln \left (1+x \right ) x +2\right )}}{x} \]
✓ Solution by Mathematica
Time used: 0.291 (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]
\[ y(x)\to \frac {\sqrt {2 x \log (x)+6 x \log (x+1)-6 x \log (2)+4}}{\sqrt {x}}-1 \]