60.1.135 problem 138

Internal problem ID [10149]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 138
Date solved : Sunday, March 30, 2025 at 03:20:05 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 11

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

\[ y = \tan \left (\ln \left (x \right )+c_1 \right ) x \]

✓ Mathematica. Time used: 0.079 (sec). Leaf size: 29

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

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{K[1]^2+1}dK[1]=\log (x)+c_1,y(x)\right ] \]

✓ Sympy. Time used: 0.306 (sec). Leaf size: 27

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

\[ y{\left (x \right )} = \frac {x \left (i C_{1} + i e^{2 i \log {\left (x \right )}}\right )}{C_{1} - e^{2 i \log {\left (x \right )}}} \]