Internal problem ID [1079]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {2 y+3 \left (x^{2}+x^{2} y^{3}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 29
dsolve((2*y(x))+3*(x^2+x^2*y(x)^3)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-\frac {x \operatorname {LambertW}\left ({\mathrm e}^{\frac {2}{x}-2 c_{1}}\right )+2 c_{1} x -2}{3 x}} \]
✓ Solution by Mathematica
Time used: 4.329 (sec). Leaf size: 82
DSolve[(2*y[x])+3*(x^2+x^2*y[x]^3)*y'[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*}