Internal problem ID [3635]
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]
\[ \boxed {x \left (-x^{4}+1\right ) y^{\prime }-2 x \left (x^{2}-y^{2}\right )-\left (-x^{4}+1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = -\tanh \left (\frac {\ln \left (x +1\right )}{2}-\frac {\ln \left (x^{2}+1\right )}{2}+\frac {\ln \left (x -1\right )}{2}+2 c_{1} \right ) x \]
✓ Solution by Mathematica
Time used: 0.329 (sec). Leaf size: 58
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 \left (x^2+e^{2 c_1} \left (x^2-1\right )+1\right )}{-x^2+e^{2 c_1} \left (x^2-1\right )-1} \\ y(x)\to -x \\ y(x)\to x \\ \end{align*}