Internal problem ID [3933]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 8
Problem number: Differential equations with Linear Coefficients. Exercise 8.1, page
69.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {x +2 y-4-\left (2 x -4 y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.026 (sec). Leaf size: 31
dsolve((x+2*y(x)-4)-(2*x-4*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = 1-\frac {\tan \left (\RootOf \left (2 \textit {\_Z} +\ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )+2 \ln \left (x -2\right )+2 c_{1}\right )\right ) \left (x -2\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.057 (sec). Leaf size: 63
DSolve[(x+2*y[x]-4)-(2*x-4*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 \text {ArcTan}\left (\frac {-2 y(x)-x+4}{x-2 y(x)}\right )+\log \left (\frac {x^2+4 y(x)^2-8 y(x)-4 x+8}{2 (x-2)^2}\right )+2 \log (x-2)+c_1=0,y(x)\right ] \]