29.13.19 problem 373

Internal problem ID [4973]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 13
Problem number : 373
Date solved : Monday, January 27, 2025 at 10:00:38 AM
CAS classification : [_linear]

\begin{align*} x \left (-x^{3}+1\right ) y^{\prime }&=2 x -\left (-4 x^{3}+1\right ) y \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 21

dsolve(x*(-x^3+1)*diff(y(x),x) = 2*x-(-4*x^3+1)*y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {-x^{2}+c_{1}}{x^{4}-x} \]

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 21

DSolve[x(1-x^3)D[y[x],x]==2 x-(1-4 x^3)y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^2+c_1}{x-x^4} \]