Internal problem ID [3147]
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]
\[ \boxed {y^{\prime }-\frac {x^{3} {\mathrm e}^{x^{2}}}{y \ln \left (y\right )}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 54
dsolve(diff(y(x),x)=(x^3*exp(x^2))/(y(x)*ln(y(x))),y(x), singsol=all)
\[ y \left (x \right ) = \sqrt {2}\, \sqrt {\frac {{\mathrm e}^{x^{2}} x^{2}-{\mathrm e}^{x^{2}}+2 c_{1}}{\operatorname {LambertW}\left (2 \left ({\mathrm e}^{x^{2}} x^{2}-{\mathrm e}^{x^{2}}+2 c_{1} \right ) {\mathrm e}^{-1}\right )}} \]
✓ Solution by Mathematica
Time used: 60.191 (sec). Leaf size: 106
DSolve[y'[x]==(x^3*Exp[x^2])/(y[x]*Log[y[x]]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {2 e^{x^2} \left (x^2-1\right )+4 c_1}}{\sqrt {W\left (\frac {2 e^{x^2} \left (x^2-1\right )+4 c_1}{e}\right )}} \\ y(x)\to \frac {\sqrt {2 e^{x^2} \left (x^2-1\right )+4 c_1}}{\sqrt {W\left (\frac {2 e^{x^2} \left (x^2-1\right )+4 c_1}{e}\right )}} \\ \end{align*}