40.3.22 problem 25 (g)

Internal problem ID [6626]
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 (g)
Date solved : Monday, January 27, 2025 at 02:16:17 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y x -2 y^{2}-\left (x^{2}-3 y x \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 19

dsolve((x*y(x)-2*y(x)^2)-(x^2-3*x*y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = -\frac {x}{3 \operatorname {LambertW}\left (-\frac {{\mathrm e}^{\frac {c_1}{3}} x^{{1}/{3}}}{3}\right )} \]

✓ Solution by Mathematica

Time used: 4.571 (sec). Leaf size: 37

DSolve[(x*y[x]-2*y[x]^2)-(x^2-3*x*y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {x}{3 W\left (-\frac {1}{3} e^{-1-\frac {c_1}{3}} \sqrt [3]{x}\right )} \\ y(x)\to 0 \\ \end{align*}