Internal problem ID [5334]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 5. Existence and uniqueness of solutions to first order equations. Page
198
Problem number: 2(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {2 y^{3}+2+3 x y^{2} y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 99
dsolve((2*y(x)^3+2)+(3*x*y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\left (\left (-x^{2}+c_{1}\right ) x \right )^{\frac {1}{3}}}{x} \\ y \relax (x ) = -\frac {\left (\left (-x^{2}+c_{1}\right ) x \right )^{\frac {1}{3}}}{2 x}-\frac {i \sqrt {3}\, \left (\left (-x^{2}+c_{1}\right ) x \right )^{\frac {1}{3}}}{2 x} \\ y \relax (x ) = -\frac {\left (\left (-x^{2}+c_{1}\right ) x \right )^{\frac {1}{3}}}{2 x}+\frac {i \sqrt {3}\, \left (\left (-x^{2}+c_{1}\right ) x \right )^{\frac {1}{3}}}{2 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.455 (sec). Leaf size: 215
DSolve[(3*y[x]^3+2)+(3*x*y[x]^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt [3]{-\frac {1}{3}} \sqrt [3]{-2 x^3+e^{9 c_1}}}{x} \\ y(x)\to \frac {\sqrt [3]{-2 x^3+e^{9 c_1}}}{\sqrt [3]{3} x} \\ y(x)\to \frac {(-1)^{2/3} \sqrt [3]{-2 x^3+e^{9 c_1}}}{\sqrt [3]{3} x} \\ y(x)\to \sqrt [3]{-\frac {2}{3}} \\ y(x)\to -\sqrt [3]{\frac {2}{3}} \\ y(x)\to -(-1)^{2/3} \sqrt [3]{\frac {2}{3}} \\ y(x)\to \frac {\sqrt [3]{-\frac {2}{3}} x^2}{\left (-x^3\right )^{2/3}} \\ y(x)\to \frac {\sqrt [3]{\frac {2}{3}} \sqrt [3]{-x^3}}{x} \\ y(x)\to \frac {(-1)^{2/3} \sqrt [3]{\frac {2}{3}} \sqrt [3]{-x^3}}{x} \\ \end{align*}