Internal problem ID [15065]
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: 176.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational]
\[ \boxed {6 y^{2} x +\left (6 x^{2} y+4 y^{3}\right ) y^{\prime }=-3 x^{2}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 125
dsolve((3*x^2+6*x*y(x)^2)+(6*x^2*y(x)+4*y(x)^3)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {\sqrt {-6 x^{2}-2 \sqrt {9 x^{4}-4 x^{3}-4 c_{1}}}}{2} \\ y \left (x \right ) &= \frac {\sqrt {-6 x^{2}-2 \sqrt {9 x^{4}-4 x^{3}-4 c_{1}}}}{2} \\ y \left (x \right ) &= -\frac {\sqrt {-6 x^{2}+2 \sqrt {9 x^{4}-4 x^{3}-4 c_{1}}}}{2} \\ y \left (x \right ) &= \frac {\sqrt {-6 x^{2}+2 \sqrt {9 x^{4}-4 x^{3}-4 c_{1}}}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 5.982 (sec). Leaf size: 163
DSolve[(3*x^2+6*x*y[x]^2)+(6*x^2*y[x]+4*y[x]^3)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-3 x^2-\sqrt {9 x^4-4 x^3+4 c_1}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-3 x^2-\sqrt {9 x^4-4 x^3+4 c_1}}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {-3 x^2+\sqrt {9 x^4-4 x^3+4 c_1}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-3 x^2+\sqrt {9 x^4-4 x^3+4 c_1}}}{\sqrt {2}} \\ \end{align*}