32.2.1 problem Differential equations with Linear Coefficients. Exercise 8.1, page 69

Internal problem ID [5785]
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
Date solved : Monday, January 27, 2025 at 01:17:55 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.056 (sec). Leaf size: 31

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

\[ y \left (x \right ) = 1-\frac {\tan \left (\operatorname {RootOf}\left (2 \textit {\_Z} +\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+2 \ln \left (x -2\right )+2 c_{1} \right )\right ) \left (x -2\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.062 (sec). Leaf size: 63

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

\[ \text {Solve}\left [2 \arctan \left (\frac {-2 y(x)-x+4}{x-2 y(x)}\right )+\log \left (\frac {x^2+4 y(x)^2-8 y(x)-4 x+8}{2 (x-2)^2}\right )+2 \log (x-2)+c_1=0,y(x)\right ] \]