Internal problem ID [5283]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {y x -2 y^{2}-\left (x^{2}-3 y x \right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve((x*y(x)-2*y(x)^2)-(x^2-3*x*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y = {\mathrm e}^{\operatorname {LambertW}\left (-\frac {{\mathrm e}^{\frac {c_{1}}{3}} x^{\frac {1}{3}}}{3}\right )-\frac {c_{1}}{3}-\frac {\ln \left (x \right )}{3}} x \]
✓ Solution by Mathematica
Time used: 4.722 (sec). Leaf size: 35
DSolve[(x*y[x]-2*y[x]^2)-(x^2-3*x*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x}{3 W\left (-\frac {1}{3} e^{-\frac {c_1}{3}} \sqrt [3]{x}\right )} y(x)\to 0 \end{align*}