48.4.5 problem Problem 3.6

Internal problem ID [7547]
Book : THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section : Chapter 3. Ordinary Differential Equations. Section 3.6 Summary and Problems. Page 218
Problem number : Problem 3.6
Date solved : Monday, January 27, 2025 at 03:05:11 PM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Solution by Maple

Time used: 0.143 (sec). Leaf size: 33

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

\[ y = \frac {{\mathrm e}^{-2 c_{1}} x}{\sqrt {-\frac {x^{4} {\mathrm e}^{-4 c_{1}}}{\operatorname {LambertW}\left (-x^{4} {\mathrm e}^{-4 c_{1}}\right )}}} \]

✓ Solution by Mathematica

Time used: 4.510 (sec). Leaf size: 60

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

\begin{align*} y(x)\to -\frac {i \sqrt {W\left (-e^{-2 c_1} x^4\right )}}{x} \\ y(x)\to \frac {i \sqrt {W\left (-e^{-2 c_1} x^4\right )}}{x} \\ y(x)\to 0 \\ \end{align*}