60.1.170 problem 173

Internal problem ID [10184]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 173
Date solved : Sunday, March 30, 2025 at 03:24:27 PM
CAS classification : [_rational, _Riccati]

\begin{align*} x^{3} y^{\prime }-x^{6} y^{2}-\left (2 x -3\right ) x^{2} y+3&=0 \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 27

ode:=x^3*diff(y(x),x)-x^6*y(x)^2-(2*x-3)*x^2*y(x)+3 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-3 \,{\mathrm e}^{4 x} c_1 -3}{x^{3} \left ({\mathrm e}^{4 x} c_1 -3\right )} \]

✓ Mathematica. Time used: 0.18 (sec). Leaf size: 34

ode=x^3*D[y[x],x] - x^6*y[x]^2 - (2*x-3)*x^2*y[x] + 3==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {-3+\frac {1}{\frac {1}{4}+c_1 e^{4 x}}}{x^3} \\ y(x)\to -\frac {3}{x^3} \\ \end{align*}

✓ Sympy. Time used: 0.341 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**6*y(x)**2 + x**3*Derivative(y(x), x) - x**2*(2*x - 3)*y(x) + 3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} + 3 e^{4 x}}{x^{3} \left (C_{1} - e^{4 x}\right )} \]