Internal problem ID [4019]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous
Methods
Problem number: Exercise 12.6, page 103.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _dAlembert]
Solve \begin {gather*} \boxed {\left (x -y\right )^{2} y^{\prime }-4=0} \end {gather*}
✓ Solution by Maple
Time used: 0.797 (sec). Leaf size: 27
dsolve((x-y(x))^2*diff(y(x),x)=4,y(x), singsol=all)
\[ y \relax (x )-\ln \left (-x +y \relax (x )+2\right )+\ln \left (-x +y \relax (x )-2\right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.287 (sec). Leaf size: 36
DSolve[(x-y[x])^2*y'[x]==4,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [y(x)-4 \left (\frac {1}{4} \log (y(x)-x+2)-\frac {1}{4} \log (-y(x)+x+2)\right )=c_1,y(x)\right ] \]