Internal problem ID [4059]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous
Methods
Problem number: Exercise 12.46, page 103.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _exact, _rational, _Bernoulli]
Solve \begin {gather*} \boxed {3 y^{2} y^{\prime } x +y^{3}-2 x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 99
dsolve(3*x*y(x)^2*diff(y(x),x)+y(x)^3-2*x=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\left (\left (x^{2}+c_{1}\right ) x^{2}\right )^{\frac {1}{3}}}{x} \\ y \relax (x ) = -\frac {\left (\left (x^{2}+c_{1}\right ) x^{2}\right )^{\frac {1}{3}}}{2 x}-\frac {i \sqrt {3}\, \left (\left (x^{2}+c_{1}\right ) x^{2}\right )^{\frac {1}{3}}}{2 x} \\ y \relax (x ) = -\frac {\left (\left (x^{2}+c_{1}\right ) x^{2}\right )^{\frac {1}{3}}}{2 x}+\frac {i \sqrt {3}\, \left (\left (x^{2}+c_{1}\right ) x^{2}\right )^{\frac {1}{3}}}{2 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.316 (sec). Leaf size: 72
DSolve[3*x*y[x]^2*y'[x]+y[x]^3-2*x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt [3]{x^2+c_1}}{\sqrt [3]{x}} \\ y(x)\to -\frac {\sqrt [3]{-1} \sqrt [3]{x^2+c_1}}{\sqrt [3]{x}} \\ y(x)\to \frac {(-1)^{2/3} \sqrt [3]{x^2+c_1}}{\sqrt [3]{x}} \\ \end{align*}