Internal problem ID [12152]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 1, First-Order Differential Equations. Problems page 88
Problem number: Problem 55.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {3 y^{2}+2 y \left (y^{2}-3 x \right ) y^{\prime }=x} \]
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 101
dsolve((3*y(x)^2-x)+(2*y(x))*(y(x)^2-3*x)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {\sqrt {2 c_{1} -2 \sqrt {c_{1} \left (c_{1} -8 x \right )}-4 x}}{2} \\ y \left (x \right ) &= \frac {\sqrt {2 c_{1} -2 \sqrt {c_{1} \left (c_{1} -8 x \right )}-4 x}}{2} \\ y \left (x \right ) &= -\frac {\sqrt {2 c_{1} +2 \sqrt {c_{1} \left (c_{1} -8 x \right )}-4 x}}{2} \\ y \left (x \right ) &= \frac {\sqrt {2 c_{1} +2 \sqrt {c_{1} \left (c_{1} -8 x \right )}-4 x}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 15.503 (sec). Leaf size: 185
DSolve[(3*y[x]^2-x)+(2*y[x])*(y[x]^2-3*x)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-2 x-e^{\frac {c_1}{2}} \sqrt {8 x+e^{c_1}}-e^{c_1}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-2 x-e^{\frac {c_1}{2}} \sqrt {8 x+e^{c_1}}-e^{c_1}}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {-2 x+e^{\frac {c_1}{2}} \sqrt {8 x+e^{c_1}}-e^{c_1}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-2 x+e^{\frac {c_1}{2}} \sqrt {8 x+e^{c_1}}-e^{c_1}}}{\sqrt {2}} \\ \end{align*}