12.7.19 problem 20

Internal problem ID [1729]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Integrating factors. Section 2.6 Page 91
Problem number : 20
Date solved : Monday, January 27, 2025 at 05:33:26 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 30

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

\[ y = {\mathrm e}^{-\frac {x \operatorname {LambertW}\left ({\mathrm e}^{\frac {-2 c_1 x +2}{x}}\right )+2 c_1 x -2}{3 x}} \]

✓ Solution by Mathematica

Time used: 3.841 (sec). Leaf size: 82

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

\begin{align*} y(x)\to \sqrt [3]{W\left (e^{\frac {2}{x}+3 c_1}\right )} \\ y(x)\to -\sqrt [3]{-1} \sqrt [3]{W\left (e^{\frac {2}{x}+3 c_1}\right )} \\ y(x)\to (-1)^{2/3} \sqrt [3]{W\left (e^{\frac {2}{x}+3 c_1}\right )} \\ y(x)\to 0 \\ \end{align*}