Internal problem ID [11200]
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 19.
Summary. Page 29
Problem number: Ex 21.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {3 y x^{2}+\left (x^{3}+x^{3} y^{2}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve(3*x^2*y(x)+(x^3+x^3*y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {1}{\sqrt {\frac {1}{\operatorname {LambertW}\left (\frac {c_{1}}{x^{6}}\right )}}} \]
✓ Solution by Mathematica
Time used: 6.245 (sec). Leaf size: 46
DSolve[3*x^2*y[x]+(x^3+x^3*y[x]^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {W\left (\frac {e^{2 c_1}}{x^6}\right )} y(x)\to \sqrt {W\left (\frac {e^{2 c_1}}{x^6}\right )} y(x)\to 0 \end{align*}