Internal problem ID [5272]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary
problems. Page 33
Problem number: 24 (p).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {y \left (x -2 y\right )-x^{2} y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(y(x)*(x-2*y(x))-x^2*diff(y(x),x)=0,y(x), singsol=all)
\[ y = \frac {x}{2 \ln \left (x \right )+c_{1}} \]
✓ Solution by Mathematica
Time used: 0.145 (sec). Leaf size: 21
DSolve[y[x]*(x-2*y[x])-x^2*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x}{2 \log (x)+c_1} y(x)\to 0 \end{align*}