12.6.11 problem 11

Internal problem ID [1690]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number : 11
Date solved : Monday, January 27, 2025 at 05:28:03 AM
CAS classification : [_separable]

\begin{align*} \frac {1}{x}+2 x +\left (\frac {1}{y}+2 y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 56

dsolve((1/x+2*x)+(1/y(x)+2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 5.840 (sec). Leaf size: 71

DSolve[(1/x+2*x)+(1/y[x]+2*y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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