Internal problem ID [3905]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 23
Problem number: 658.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _exact, _rational, _Bernoulli]
\[ \boxed {6 x y^{2} y^{\prime }+2 y^{3}=-x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 92
dsolve(6*x*y(x)^2*diff(y(x),x)+x+2*y(x)^3 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {2^{\frac {1}{3}} {\left (-\left (x^{2}-4 c_{1} \right ) x^{2}\right )}^{\frac {1}{3}}}{2 x} \\ y \left (x \right ) &= -\frac {2^{\frac {1}{3}} {\left (-\left (x^{2}-4 c_{1} \right ) x^{2}\right )}^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{4 x} \\ y \left (x \right ) &= \frac {2^{\frac {1}{3}} {\left (-\left (x^{2}-4 c_{1} \right ) x^{2}\right )}^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{4 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.241 (sec). Leaf size: 99
DSolve[6 x y[x]^2 y'[x]+x+2 y[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt [3]{-x^2+4 c_1}}{2^{2/3} \sqrt [3]{x}} \\ y(x)\to -\frac {\sqrt [3]{-1} \sqrt [3]{-x^2+4 c_1}}{2^{2/3} \sqrt [3]{x}} \\ y(x)\to \frac {(-1)^{2/3} \sqrt [3]{-x^2+4 c_1}}{2^{2/3} \sqrt [3]{x}} \\ \end{align*}