29.13.21 problem 375

Internal problem ID [4975]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 13
Problem number : 375
Date solved : Monday, January 27, 2025 at 10:00:42 AM
CAS classification : [_rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 72

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

\[ y \left (x \right ) = \frac {\sqrt {x^{2}-1}\, x}{\sqrt {x -1}\, \sqrt {x +1}\, c_{1} \sqrt {x^{2}-1}-3 \ln \left (x +\sqrt {x^{2}-1}\right ) x^{2}+3 \sqrt {x^{2}-1}\, x +3 \ln \left (x +\sqrt {x^{2}-1}\right )} \]

✓ Solution by Mathematica

Time used: 0.276 (sec). Leaf size: 59

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

\begin{align*} y(x)\to \frac {x}{-3 \sqrt {1-x^2} \arctan \left (\frac {x}{\sqrt {1-x^2}}\right )+c_1 \sqrt {1-x^2}+3 x} \\ y(x)\to 0 \\ \end{align*}