77.1.40 problem 57 (page 103)

Internal problem ID [17930]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 57 (page 103)
Date solved : Tuesday, January 28, 2025 at 11:13:41 AM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} \left (x^{2} y^{2}-1\right ) y^{\prime }+2 x y^{3}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.075 (sec). Leaf size: 45

dsolve((x^2*y(x)^2-1)*diff(y(x),x)+2*x*y(x)^3=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {-\sqrt {c_{1}^{2}-4 x^{2}}+c_{1}}{2 x^{2}} \\ y &= \frac {\sqrt {c_{1}^{2}-4 x^{2}}+c_{1}}{2 x^{2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.296 (sec). Leaf size: 64

DSolve[(x^2*y[x]^2-1)*D[y[x],x]+2*x*y[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {c_1-\sqrt {-4 x^2+c_1{}^2}}{2 x^2} \\ y(x)\to \frac {\sqrt {-4 x^2+c_1{}^2}+c_1}{2 x^2} \\ y(x)\to 0 \\ \end{align*}