32.6.6 problem Exercise 12.6, page 103

Internal problem ID [5871]
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
Date solved : Monday, January 27, 2025 at 01:22:32 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.287 (sec). Leaf size: 27

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

\[ y \left (x \right )+\ln \left (-x +y \left (x \right )-2\right )-\ln \left (-x +y \left (x \right )+2\right )-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.223 (sec). Leaf size: 36

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

\[ \text {Solve}\left [y(x)-4 \left (\frac {1}{4} \log (y(x)-x+2)-\frac {1}{4} \log (-y(x)+x+2)\right )=c_1,y(x)\right ] \]