29.13.22 problem 376

Internal problem ID [4976]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 13
Problem number : 376
Date solved : Monday, January 27, 2025 at 10:00:44 AM
CAS classification : [_separable]

\begin{align*} x \left (-2 x^{3}+1\right ) y^{\prime }&=2 \left (-x^{3}+1\right ) y \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 18

dsolve(x*(-2*x^3+1)*diff(y(x),x) = 2*(-x^3+1)*y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {c_{1} x^{2}}{\left (2 x^{3}-1\right )^{{1}/{3}}} \]

✓ Solution by Mathematica

Time used: 0.051 (sec). Leaf size: 27

DSolve[x(1-2 x^3) D[y[x],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*}