Internal problem ID [15084]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 7, Total differential equations. The integrating factor. Exercises page
61
Problem number: 196.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {3 y^{2}+\left (2 y^{3}-6 y x \right ) y^{\prime }=x} \]
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 101
dsolve(( 3*y(x)^2-x)+( 2*y(x)^3-6*x*y(x) )*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {\sqrt {-2 \sqrt {c_{1} \left (c_{1} -8 x \right )}+2 c_{1} -4 x}}{2} \\ y \left (x \right ) &= \frac {\sqrt {-2 \sqrt {c_{1} \left (c_{1} -8 x \right )}+2 c_{1} -4 x}}{2} \\ y \left (x \right ) &= -\frac {\sqrt {2 \sqrt {c_{1} \left (c_{1} -8 x \right )}+2 c_{1} -4 x}}{2} \\ y \left (x \right ) &= \frac {\sqrt {2 \sqrt {c_{1} \left (c_{1} -8 x \right )}+2 c_{1} -4 x}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 11.553 (sec). Leaf size: 185
DSolve[( 3*y[x]^2-x)+( 2*y[x]^3-6*x*y[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*}