26.1.2 problem 1.b

Internal problem ID [4242]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, section 7, page 37
Problem number : 1.b
Date solved : Monday, January 27, 2025 at 08:43:51 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} x^{2} y^{\prime }-2 y x -2 y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

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

\[ y \left (x \right ) = \frac {x^{2}}{c_{1} -2 x} \]

✓ Solution by Mathematica

Time used: 0.155 (sec). Leaf size: 22

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

\begin{align*} y(x)\to \frac {x^2}{-2 x+c_1} \\ y(x)\to 0 \\ \end{align*}