Internal problem ID [6235]
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]
\[ \boxed {y^{3} x +3 y^{\prime } y^{2}=-x^{3}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 81
dsolve((x^3+x*y(x)^3)+(3*y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \left ({\mathrm e}^{-\frac {x^{2}}{2}} c_{1} -x^{2}+2\right )^{\frac {1}{3}} \\ y \left (x \right ) &= -\frac {\left ({\mathrm e}^{-\frac {x^{2}}{2}} c_{1} -x^{2}+2\right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{2} \\ y \left (x \right ) &= \frac {\left ({\mathrm e}^{-\frac {x^{2}}{2}} c_{1} -x^{2}+2\right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 10.689 (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*}