47.2.55 problem 51

Internal problem ID [7471]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems. page 12
Problem number : 51
Date solved : Monday, January 27, 2025 at 03:01:28 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: 0.020 (sec). Leaf size: 33

dsolve(y(x)*(x^2*y(x)^2+1)+(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: 4.294 (sec). Leaf size: 60

DSolve[y[x]*(x^2*y[x]^2+1)+(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*}