Internal problem ID [98]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.6, Substitution methods and exact equations. Page 74
Problem number: 20.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {2 x y^{3}+y^{2} y^{\prime }-6 x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 88
dsolve(2*x*y(x)^3+y(x)^2*diff(y(x),x) = 6*x,y(x), singsol=all)
\begin{align*} y \relax (x ) = \left ({\mathrm e}^{-3 x^{2}} c_{1}+3\right )^{\frac {1}{3}} \\ y \relax (x ) = -\frac {\left ({\mathrm e}^{-3 x^{2}} c_{1}+3\right )^{\frac {1}{3}}}{2}-\frac {i \sqrt {3}\, \left ({\mathrm e}^{-3 x^{2}} c_{1}+3\right )^{\frac {1}{3}}}{2} \\ y \relax (x ) = -\frac {\left ({\mathrm e}^{-3 x^{2}} c_{1}+3\right )^{\frac {1}{3}}}{2}+\frac {i \sqrt {3}\, \left ({\mathrm e}^{-3 x^{2}} c_{1}+3\right )^{\frac {1}{3}}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.914 (sec). Leaf size: 115
DSolve[2*x*y[x]^3+y[x]^2*y'[x] == 6*x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt [3]{3+e^{-3 x^2+3 c_1}} \\ y(x)\to -\sqrt [3]{-1} \sqrt [3]{3+e^{-3 x^2+3 c_1}} \\ y(x)\to (-1)^{2/3} \sqrt [3]{3+e^{-3 x^2+3 c_1}} \\ y(x)\to -\sqrt [3]{-3} \\ y(x)\to \sqrt [3]{3} \\ y(x)\to (-1)^{2/3} \sqrt [3]{3} \\ \end{align*}