Internal problem ID [4570]
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 12.49, page 103.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (2 y^{3}+y\right ) y^{\prime }=2 x^{3}+x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 113
dsolve((2*y(x)^3+y(x))*diff(y(x),x)-2*x^3-x=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -\frac {\sqrt {-2-2 \sqrt {4 x^{4}+4 x^{2}+8 c_{1} +1}}}{2} y \left (x \right ) = \frac {\sqrt {-2-2 \sqrt {4 x^{4}+4 x^{2}+8 c_{1} +1}}}{2} y \left (x \right ) = -\frac {\sqrt {-2+2 \sqrt {4 x^{4}+4 x^{2}+8 c_{1} +1}}}{2} y \left (x \right ) = \frac {\sqrt {-2+2 \sqrt {4 x^{4}+4 x^{2}+8 c_{1} +1}}}{2} \end{align*}
✓ Solution by Mathematica
Time used: 2.313 (sec). Leaf size: 151
DSolve[(2*y[x]^3+y[x])*y'[x]-2*x^3-x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-1-\sqrt {4 x^4+4 x^2+1+8 c_1}}}{\sqrt {2}} y(x)\to \frac {\sqrt {-1-\sqrt {4 x^4+4 x^2+1+8 c_1}}}{\sqrt {2}} y(x)\to -\frac {\sqrt {-1+\sqrt {4 x^4+4 x^2+1+8 c_1}}}{\sqrt {2}} y(x)\to \frac {\sqrt {-1+\sqrt {4 x^4+4 x^2+1+8 c_1}}}{\sqrt {2}} \end{align*}