28.1.103 problem 126

Internal problem ID [4409]
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 : 126
Date solved : Monday, January 27, 2025 at 09:15:04 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} y^{\prime }&=\frac {1}{y x +x^{3} y^{3}} \end{align*}

✓ Solution by Maple

Time used: 0.303 (sec). Leaf size: 68

dsolve(diff(y(x),x)=1/(x*y(x)+x^3*y(x)^3),y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {\sqrt {\operatorname {LambertW}\left (c_{1} {\mathrm e}^{-\frac {\left (x -1\right ) \left (x +1\right )}{x^{2}}}\right ) x^{2}+x^{2}-1}}{x} \\ y \left (x \right ) &= -\frac {\sqrt {\operatorname {LambertW}\left (c_{1} {\mathrm e}^{-\frac {\left (x -1\right ) \left (x +1\right )}{x^{2}}}\right ) x^{2}+x^{2}-1}}{x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 60.135 (sec). Leaf size: 68

DSolve[D[y[x],x]==1/(x*y[x]+x^3*y[x]^3),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {x^2 W\left (8 c_1 e^{\frac {1}{x^2}-1}\right )+x^2-1}}{x} \\ y(x)\to \frac {\sqrt {x^2 W\left (8 c_1 e^{\frac {1}{x^2}-1}\right )+x^2-1}}{x} \\ \end{align*}