Internal problem ID [3127]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 13
Problem number: 379.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _rational, _Riccati]
Solve \begin {gather*} \boxed {x \left (1-x^{4}\right ) y^{\prime }-2 x \left (x^{2}-y^{2}\right )-\left (1-x^{4}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 32
dsolve(x*(-x^4+1)*diff(y(x),x) = 2*x*(x^2-y(x)^2)+(-x^4+1)*y(x),y(x), singsol=all)
\[ y \relax (x ) = -\tanh \left (-\frac {\ln \left (x^{2}+1\right )}{2}+\frac {\ln \left (x -1\right )}{2}+\frac {\ln \left (x +1\right )}{2}+2 c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 0.313 (sec). Leaf size: 46
DSolve[x(1-x^4)y'[x]==2 x(x^2-y[x]^2)+(1-x^4) y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^3 \cosh (c_1)-x \sinh (c_1)}{\cosh (c_1)-x^2 \sinh (c_1)} \\ y(x)\to -x \\ y(x)\to x \\ \end{align*}