54.1.169 problem 172

Internal problem ID [11483]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 172
Date solved : Tuesday, September 30, 2025 at 08:35:48 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Riccati]

\begin{align*} x^{3} y^{\prime }-x^{4} y^{2}+x^{2} y+20&=0 \end{align*}

✓ Maple. Time used: 0.116 (sec). Leaf size: 26

ode:=x^3*diff(y(x),x)-y(x)^2*x^4+x^2*y(x)+20 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {5 x^{9}+4 c_1}{x^{2} \left (-x^{9}+c_1 \right )} \]

✓ Mathematica. Time used: 0.099 (sec). Leaf size: 36

ode=x^3*D[y[x],x] - x^4*y[x]^2 + x^2*y[x] + 20==0; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.210 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**4*y(x)**2 + x**3*Derivative(y(x), x) + x**2*y(x) + 20,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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