Internal problem ID [3097]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 12
Problem number: 349.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Riccati]
Solve \begin {gather*} \boxed {y^{\prime } x^{3}+20+x^{2} y \left (1-x^{2} y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.157 (sec). Leaf size: 26
dsolve(x^3*diff(y(x),x)+20+x^2*y(x)*(1-x^2*y(x)) = 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {5 x^{9}+4 c_{1}}{x^{2} \left (-x^{9}+c_{1}\right )} \]
✓ Solution by Mathematica
Time used: 0.153 (sec). Leaf size: 33
DSolve[x^3 y'[x]+20+x^2 y[x](1-x^2 y[x])==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {4}{x^2}-\frac {9 x^7}{x^9+c_1} \\ y(x)\to \frac {4}{x^2} \\ \end{align*}