Internal problem ID [4567]
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]
\[ \boxed {3 x y^{2} y^{\prime }+y^{3}=2 x} \]
✓ Solution by Maple
Time used: 0.0 (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 \left (x \right ) = \frac {{\left (\left (x^{2}+c_{1} \right ) x^{2}\right )}^{\frac {1}{3}}}{x} y \left (x \right ) = -\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 \left (x \right ) = -\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: 0.224 (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*}