Internal problem ID [3124]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 13
Problem number: 376.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x \left (-2 x^{3}+1\right ) y^{\prime }-2 \left (-x^{3}+1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(x*(-2*x^3+1)*diff(y(x),x) = 2*(-x^3+1)*y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} x^{2}}{\left (2 x^{3}-1\right )^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 27
DSolve[x(1-2 x^3) y'[x]==2(1-x^3)y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1 x^2}{\sqrt [3]{1-2 x^3}} \\ y(x)\to 0 \\ \end{align*}