Internal problem ID [3392]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 23
Problem number: 653.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _exact, _rational, _Bernoulli]
Solve \begin {gather*} \boxed {3 y^{\prime } y^{2} x -2 x +y^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 99
dsolve(3*x*y(x)^2*diff(y(x),x) = 2*x-y(x)^3,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\left (\left (x^{2}+c_{1}\right ) x^{2}\right )^{\frac {1}{3}}}{x} \\ y \relax (x ) = -\frac {\left (\left (x^{2}+c_{1}\right ) x^{2}\right )^{\frac {1}{3}}}{2 x}-\frac {i \sqrt {3}\, \left (\left (x^{2}+c_{1}\right ) x^{2}\right )^{\frac {1}{3}}}{2 x} \\ y \relax (x ) = -\frac {\left (\left (x^{2}+c_{1}\right ) x^{2}\right )^{\frac {1}{3}}}{2 x}+\frac {i \sqrt {3}\, \left (\left (x^{2}+c_{1}\right ) x^{2}\right )^{\frac {1}{3}}}{2 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.204 (sec). Leaf size: 72
DSolve[3 x y[x]^2 y'[x]==2 x-y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt [3]{x^2+c_1}}{\sqrt [3]{x}} \\ y(x)\to -\frac {\sqrt [3]{-1} \sqrt [3]{x^2+c_1}}{\sqrt [3]{x}} \\ y(x)\to \frac {(-1)^{2/3} \sqrt [3]{x^2+c_1}}{\sqrt [3]{x}} \\ \end{align*}