62.12.20 problem Ex 21

Internal problem ID [12866]
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
Date solved : Tuesday, January 28, 2025 at 04:29:05 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.033 (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)
 

\[ y = \frac {1}{\sqrt {\frac {1}{\operatorname {LambertW}\left (\frac {c_{1}}{x^{6}}\right )}}} \]

✓ Solution by Mathematica

Time used: 1.514 (sec). Leaf size: 46

DSolve[3*x^2*y[x]+(x^3+x^3*y[x]^2)*D[y[x],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*}