1.171 problem 172

Internal problem ID [7752]

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]

Solve \begin {gather*} \boxed {x^{3} y^{\prime }-x^{4} y^{2}+y x^{2}+20=0} \end {gather*}

Solution by Maple

Time used: 0.984 (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)
 

\[ y \relax (x ) = \frac {5 x^{9}+4 c_{1}}{x^{2} \left (-x^{9}+c_{1}\right )} \]

Solution by Mathematica

Time used: 0.166 (sec). Leaf size: 33

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 {4}{x^2}-\frac {9 x^7}{x^9+c_1} \\ y(x)\to \frac {4}{x^2} \\ \end{align*}