Internal problem ID [15024]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 5. Homogeneous equations. Exercises page 44
Problem number: 117.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Bernoulli]
\[ \boxed {4 y^{6}-6 y^{5} x y^{\prime }=-x^{3}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 127
dsolve(4*y(x)^6+x^3=6*x*y(x)^5*diff(y(x),x),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \left (x^{3} \left (c_{1} x -1\right )\right )^{\frac {1}{6}} \\ y \left (x \right ) &= -\left (x^{3} \left (c_{1} x -1\right )\right )^{\frac {1}{6}} \\ y \left (x \right ) &= -\frac {\left (1+i \sqrt {3}\right ) \left (x^{3} \left (c_{1} x -1\right )\right )^{\frac {1}{6}}}{2} \\ y \left (x \right ) &= \frac {\left (i \sqrt {3}-1\right ) \left (x^{3} \left (c_{1} x -1\right )\right )^{\frac {1}{6}}}{2} \\ y \left (x \right ) &= -\frac {\left (i \sqrt {3}-1\right ) \left (x^{3} \left (c_{1} x -1\right )\right )^{\frac {1}{6}}}{2} \\ y \left (x \right ) &= \frac {\left (1+i \sqrt {3}\right ) \left (x^{3} \left (c_{1} x -1\right )\right )^{\frac {1}{6}}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.276 (sec). Leaf size: 144
DSolve[4*y[x]^6+x^3==6*x*y[x]^5*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {x} \sqrt [6]{-1+c_1 x} \\ y(x)\to \sqrt {x} \sqrt [6]{-1+c_1 x} \\ y(x)\to -\sqrt [3]{-1} \sqrt {x} \sqrt [6]{-1+c_1 x} \\ y(x)\to \sqrt [3]{-1} \sqrt {x} \sqrt [6]{-1+c_1 x} \\ y(x)\to -(-1)^{2/3} \sqrt {x} \sqrt [6]{-1+c_1 x} \\ y(x)\to (-1)^{2/3} \sqrt {x} \sqrt [6]{-1+c_1 x} \\ \end{align*}