Internal problem ID [10140]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 15. Page
22
Problem number: Ex 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{2} \left (3 y-6 y^{\prime } x \right )-x \left (y-2 y^{\prime } x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(y(x)^2*(3*y(x)-6*x*diff(y(x),x))-x*(y(x)-2*x*diff(y(x),x))=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {3}\, \sqrt {x}}{3} \\ y \relax (x ) = \frac {\sqrt {3}\, \sqrt {x}}{3} \\ y \relax (x ) = c_{1} \sqrt {x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 60.145 (sec). Leaf size: 69
DSolve[y[x]^2*(3*y[x]-6*x*y'[x])- x*(4*y[x]-2*x*y'[x])==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {i \sqrt {x} \sqrt {\text {ProductLog}\left (-3 e^{-3 c_1} x^3\right )}}{\sqrt {3}} \\ y(x)\to \frac {i \sqrt {x} \sqrt {\text {ProductLog}\left (-3 e^{-3 c_1} x^3\right )}}{\sqrt {3}} \\ \end{align*}