47.3.1 problem 1

Internal problem ID [7474]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.3. Exact equations problems. page 24
Problem number : 1
Date solved : Monday, January 27, 2025 at 03:01:32 PM
CAS classification : [_exact, _rational]

\begin{align*} x \left (2-9 x y^{2}\right )+y \left (4 y^{2}-6 x^{3}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 125

dsolve(x*(2-9*x*y(x)^2)+y(x)*(4*y(x)^2-6*x^3)*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= -\frac {\sqrt {6 x^{3}-2 \sqrt {9 x^{6}-4 x^{2}-4 c_{1}}}}{2} \\ y &= \frac {\sqrt {6 x^{3}-2 \sqrt {9 x^{6}-4 x^{2}-4 c_{1}}}}{2} \\ y &= -\frac {\sqrt {6 x^{3}+2 \sqrt {9 x^{6}-4 x^{2}-4 c_{1}}}}{2} \\ y &= \frac {\sqrt {6 x^{3}+2 \sqrt {9 x^{6}-4 x^{2}-4 c_{1}}}}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 5.859 (sec). Leaf size: 163

DSolve[x*(2-9*x*y[x]^2)+y[x]*(4*y[x]^2-6*x^3)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {3 x^3-\sqrt {9 x^6-4 x^2+4 c_1}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {3 x^3-\sqrt {9 x^6-4 x^2+4 c_1}}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {3 x^3+\sqrt {9 x^6-4 x^2+4 c_1}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {3 x^3+\sqrt {9 x^6-4 x^2+4 c_1}}}{\sqrt {2}} \\ \end{align*}