Internal problem ID [8508]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 172.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Riccati]
\[ \boxed {y^{\prime } x^{3}-x^{4} y^{2}+x^{2} y=-20} \]
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 26
dsolve(x^3*diff(y(x),x) - x^4*y(x)^2 + x^2*y(x) + 20=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {5 x^{9}+4 c_{1}}{\left (-x^{9}+c_{1} \right ) x^{2}} \]
✓ Solution by Mathematica
Time used: 0.16 (sec). Leaf size: 36
DSolve[x^3*y'[x] - x^4*y[x]^2 + x^2*y[x] + 20==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-5 x^9+4 c_1}{x^2 \left (x^9+c_1\right )} \\ y(x)\to \frac {4}{x^2} \\ \end{align*}