60.1.167 problem 170

Internal problem ID [10181]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 170
Date solved : Wednesday, March 05, 2025 at 08:37:55 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Riccati]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

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

\[ y = \frac {x^{2} \left (\ln \left (x \right )-c_{1} -1\right )}{\ln \left (x \right )-c_{1}} \]

✓ Mathematica. Time used: 0.17 (sec). Leaf size: 29

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

\begin{align*} y(x)\to \frac {x^2 (\log (x)-1+c_1)}{\log (x)+c_1} \\ y(x)\to x^2 \\ \end{align*}

✓ Sympy. Time used: 0.207 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = x^{2} \left (1 - 8 x^{2}\right ) \]