Internal problem ID [1019]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable
Equations. Section 2.4 Page 68
Problem number: 44.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {3 y^{2} y^{\prime } x -y^{3}-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 78
dsolve(3*x*y(x)^2*diff(y(x),x)=y(x)^3+x,y(x), singsol=all)
\begin{align*} y \relax (x ) = \left (x \ln \relax (x )+x c_{1}\right )^{\frac {1}{3}} \\ y \relax (x ) = -\frac {\left (x \ln \relax (x )+x c_{1}\right )^{\frac {1}{3}}}{2}-\frac {i \sqrt {3}\, \left (x \ln \relax (x )+x c_{1}\right )^{\frac {1}{3}}}{2} \\ y \relax (x ) = -\frac {\left (x \ln \relax (x )+x c_{1}\right )^{\frac {1}{3}}}{2}+\frac {i \sqrt {3}\, \left (x \ln \relax (x )+x c_{1}\right )^{\frac {1}{3}}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.186 (sec). Leaf size: 69
DSolve[3*x*y[x]^2*y'[x]==y[x]^3+x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt [3]{x} \sqrt [3]{\log (x)+c_1} \\ y(x)\to -\sqrt [3]{-1} \sqrt [3]{x} \sqrt [3]{\log (x)+c_1} \\ y(x)\to (-1)^{2/3} \sqrt [3]{x} \sqrt [3]{\log (x)+c_1} \\ \end{align*}