Internal problem ID [5053]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational]
Solve \begin {gather*} \boxed {x \left (2-9 y^{2} x \right )+y \left (4 y^{2}-6 x^{3}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (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 \relax (x ) = -\frac {\sqrt {6 x^{3}-2 \sqrt {9 x^{6}-4 x^{2}-4 c_{1}}}}{2} \\ y \relax (x ) = \frac {\sqrt {6 x^{3}-2 \sqrt {9 x^{6}-4 x^{2}-4 c_{1}}}}{2} \\ y \relax (x ) = -\frac {\sqrt {6 x^{3}+2 \sqrt {9 x^{6}-4 x^{2}-4 c_{1}}}}{2} \\ y \relax (x ) = \frac {\sqrt {6 x^{3}+2 \sqrt {9 x^{6}-4 x^{2}-4 c_{1}}}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 6.587 (sec). Leaf size: 163
DSolve[x*(2-9*x*y[x]^2)+y[x]*(4*y[x]^2-6*x^3)*y'[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*}