Internal problem ID [5447]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.5. Exact Equations. Page
20
Problem number: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, [_1st_order, _with_symmetry_[F(x)*G(y),0]]]
Solve \begin {gather*} \boxed {3 x^{2} \left (1+\ln \relax (y)\right )+\left (\frac {x^{3}}{y}-2 y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.024 (sec). Leaf size: 39
dsolve((3*x^2*(1+ln(y(x))))+(x^3/y(x)-2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\frac {x^{3} \LambertW \left (-\frac {2 \,{\mathrm e}^{-2} {\mathrm e}^{-\frac {2 c_{1}}{x^{3}}}}{x^{3}}\right )+2 x^{3}+2 c_{1}}{2 x^{3}}} \]
✓ Solution by Mathematica
Time used: 0.04 (sec). Leaf size: 79
DSolve[(3*x^2*(1+Log[y[x]]))+(x^3/y[x]-2*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {i x^{3/2} \sqrt {\text {ProductLog}\left (-\frac {2 e^{-2+\frac {2 c_1}{x^3}}}{x^3}\right )}}{\sqrt {2}} \\ y(x)\to \frac {i x^{3/2} \sqrt {\text {ProductLog}\left (-\frac {2 e^{-2+\frac {2 c_1}{x^3}}}{x^3}\right )}}{\sqrt {2}} \\ \end{align*}