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]
\[ \boxed {2 x y^{3}+y^{2} y^{\prime }=6 x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 66
dsolve(2*x*y(x)^3+y(x)^2*diff(y(x),x) = 6*x,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \left ({\mathrm e}^{-3 x^{2}} c_{1} +3\right )^{\frac {1}{3}} \\ y \left (x \right ) &= -\frac {\left ({\mathrm e}^{-3 x^{2}} c_{1} +3\right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{2} \\ y \left (x \right ) &= \frac {\left ({\mathrm e}^{-3 x^{2}} c_{1} +3\right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.937 (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*}