Internal problem ID [5482]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.8. Integrating Factors. Page
32
Problem number: 1(k).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
Solve \begin {gather*} \boxed {x^{3}+y^{3} x +3 y^{2} y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 113
dsolve((x^3+x*y(x)^3)+(3*y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \left ({\mathrm e}^{-\frac {x^{2}}{2}} c_{1}-x^{2}+2\right )^{\frac {1}{3}} \\ y \relax (x ) = -\frac {\left ({\mathrm e}^{-\frac {x^{2}}{2}} c_{1}-x^{2}+2\right )^{\frac {1}{3}}}{2}-\frac {i \sqrt {3}\, \left ({\mathrm e}^{-\frac {x^{2}}{2}} c_{1}-x^{2}+2\right )^{\frac {1}{3}}}{2} \\ y \relax (x ) = -\frac {\left ({\mathrm e}^{-\frac {x^{2}}{2}} c_{1}-x^{2}+2\right )^{\frac {1}{3}}}{2}+\frac {i \sqrt {3}\, \left ({\mathrm e}^{-\frac {x^{2}}{2}} c_{1}-x^{2}+2\right )^{\frac {1}{3}}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 11.311 (sec). Leaf size: 95
DSolve[(x^3+x*y[x]^3)+(3*y[x]^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt [3]{-x^2+c_1 e^{-\frac {x^2}{2}}+2} \\ y(x)\to -\sqrt [3]{-1} \sqrt [3]{-x^2+c_1 e^{-\frac {x^2}{2}}+2} \\ y(x)\to (-1)^{2/3} \sqrt [3]{-x^2+c_1 e^{-\frac {x^2}{2}}+2} \\ \end{align*}