47.3.4 problem 4

Internal problem ID [7477]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.3. Exact equations problems. page 24
Problem number : 4
Date solved : Monday, January 27, 2025 at 03:01:40 PM
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: 0.171 (sec). Leaf size: 55

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

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

✓ Solution by Mathematica

Time used: 0.047 (sec). Leaf size: 51

DSolve[(2*x+3)+(2*y[x]-2)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 1-\sqrt {-x^2-3 x+1+2 c_1} \\ y(x)\to 1+\sqrt {-x^2-3 x+1+2 c_1} \\ \end{align*}