60.1.422 problem 433

Internal problem ID [10436]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 433
Date solved : Sunday, March 30, 2025 at 04:43:11 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]

\begin{align*} \left (x y^{\prime }+y+2 x \right )^{2}-4 x y-4 x^{2}-4 a&=0 \end{align*}

✓ Maple. Time used: 0.056 (sec). Leaf size: 36

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

\begin{align*} y &= \frac {-x^{2}-a}{x} \\ y &= \frac {c_{1}^{2}+4 c_{1} x -4 a}{4 x} \\ \end{align*}

✓ Mathematica. Time used: 0.908 (sec). Leaf size: 44

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

\begin{align*} y(x)\to \frac {-a+c_1 (-2 x+c_1)}{x} \\ y(x)\to -2 \sqrt {a} \\ y(x)\to 2 \sqrt {a} \\ \end{align*}

✗ Sympy

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

Timed Out