40.3.18 problem 25 (c)

Internal problem ID [6622]
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 : 25 (c)
Date solved : Monday, January 27, 2025 at 02:16:14 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 30

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

\begin{align*} y &= \sqrt {-x \left (\ln \left (x \right )-c_1 \right )} \\ y &= -\sqrt {\left (-\ln \left (x \right )+c_1 \right ) x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.214 (sec). Leaf size: 44

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

\begin{align*} y(x)\to -\sqrt {x} \sqrt {-\log (x)+c_1} \\ y(x)\to \sqrt {x} \sqrt {-\log (x)+c_1} \\ \end{align*}