40.3.11 problem 24 (p)

Internal problem ID [6615]
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)
Date solved : Monday, January 27, 2025 at 02:15:56 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.002 (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: 0.157 (sec). Leaf size: 21

DSolve[y[x]*(x-2*y[x])-x^2*D[y[x],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*}