47.2.56 problem 52

Internal problem ID [7472]
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 : 52
Date solved : Monday, January 27, 2025 at 03:01:29 PM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} \left (x^{2}-y^{4}\right ) y^{\prime }-y x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.074 (sec). Leaf size: 97

dsolve((x^2-y(x)^4)*diff(y(x),x)-x*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 2.220 (sec). Leaf size: 122

DSolve[(x^2-y[x]^4)*D[y[x],x]-x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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