36.1.20 problem 20

Internal problem ID [6275]
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
Date solved : Monday, January 27, 2025 at 01:52:47 PM
CAS classification : [_separable]

\begin{align*} x^{2} y^{\prime }&=\frac {4 x^{2}-x -2}{\left (1+x \right ) \left (y+1\right )} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.104 (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)
 

\[ y = \frac {-x +\sqrt {2}\, \sqrt {x \left (x \ln \left (x \right )-3 \ln \left (2\right ) x +3 \ln \left (x +1\right ) x +2\right )}}{x} \]

✓ Solution by Mathematica

Time used: 0.406 (sec). Leaf size: 36

DSolve[{x^2*D[y[x],x]==(4*x^2-x-2)/((x+1)*(y[x]+1)),{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\sqrt {2 x \log (x)+6 x \log (x+1)-6 x \log (2)+4}}{\sqrt {x}}-1 \]