76.4.2 problem 2

Internal problem ID [17396]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.6 (Exact equations and integrating factors). Problems at page 100
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 10:04:28 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 x +4 y+\left (2 x -2 y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 1.801 (sec). Leaf size: 55

dsolve((2*x+4*y(x))+(2*x-2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ -\frac {\ln \left (\frac {-x^{2}-3 x y+y^{2}}{x^{2}}\right )}{2}+\frac {\sqrt {13}\, \operatorname {arctanh}\left (\frac {\left (2 y-3 x \right ) \sqrt {13}}{13 x}\right )}{13}-\ln \left (x \right )-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 40

DSolve[(2*x+4*y[x])+(2*x-2*y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {K[1]-1}{K[1]^2-3 K[1]-1}dK[1]=-\log (x)+c_1,y(x)\right ] \]