Internal problem ID [5809]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {4 y+\left (2 x -2 y\right ) y^{\prime }=-2 x} \]
✓ Solution by Maple
Time used: 0.328 (sec). Leaf size: 55
dsolve((2*x+4*y(x))+(2*x-2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ -\frac {\ln \left (\frac {-x^{2}-3 x y \left (x \right )+y \left (x \right )^{2}}{x^{2}}\right )}{2}+\frac {\sqrt {13}\, \operatorname {arctanh}\left (\frac {\left (2 y \left (x \right )-3 x \right ) \sqrt {13}}{13 x}\right )}{13}-\ln \left (x \right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 51
DSolve[(2*x+3)+(2*y[x]-2)*y'[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*}