Internal problem ID [2638]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x^{3} {\mathrm e}^{x^{2}}}{\ln \relax (y) y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 32
dsolve(diff(y(x),x)=(x^3*exp(x^2))/(y(x)*ln(y(x))),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\frac {\LambertW \left (2 \left (x^{2} {\mathrm e}^{x^{2}}-{\mathrm e}^{x^{2}}+2 c_{1}\right ) {\mathrm e}^{-1}\right )}{2}+\frac {1}{2}} \]
✓ Solution by Mathematica
Time used: 0.138 (sec). Leaf size: 71
DSolve[y'[x]==(x^3*Exp[x^2])/(y[x]*Log[y[x]]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\exp \left (\frac {1}{2} \left (1+\text {ProductLog}\left (\frac {2 e^{x^2} \left (x^2-1\right )+4 c_1}{e}\right )\right )\right ) \\ y(x)\to \exp \left (\frac {1}{2} \left (1+\text {ProductLog}\left (\frac {2 e^{x^2} \left (x^2-1\right )+4 c_1}{e}\right )\right )\right ) \\ \end{align*}