69.1.60 problem 79

Internal problem ID [14213]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 79
Date solved : Tuesday, January 28, 2025 at 06:22:15 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 13

dsolve(x^2/(x-y(x))^2*diff(y(x),x)- y(x)^2/(x-y(x))^2=0,y(x), singsol=all)
 

\[ y = \frac {x}{c_{1} x +1} \]

✓ Solution by Mathematica

Time used: 0.118 (sec). Leaf size: 21

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

\begin{align*} y(x)\to \frac {x}{1-c_1 x} \\ y(x)\to 0 \\ \end{align*}