Internal problem ID [5126]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {y \left (y^{2} x^{2}+1\right )+\left (y^{2} x^{2}-1\right ) x y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 23
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)
\[ y \relax (x ) = {\mathrm e}^{-\frac {\LambertW \left (-x^{4} {\mathrm e}^{-4 c_{1}}\right )}{2}-2 c_{1}} x \]
✓ Solution by Mathematica
Time used: 60.165 (sec). Leaf size: 55
DSolve[(x^2*y[x]^2+1)*y[x]+(x^2*y[x]^2-1)*x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {i \sqrt {\text {ProductLog}\left (-e^{-2 c_1} x^4\right )}}{x} \\ y(x)\to \frac {i \sqrt {\text {ProductLog}\left (-e^{-2 c_1} x^4\right )}}{x} \\ \end{align*}