54.2.228 problem 805

Internal problem ID [12102]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 805
Date solved : Sunday, October 12, 2025 at 02:16:18 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} y^{\prime }&=\frac {x y+y+x^{4} \sqrt {y^{2}+x^{2}}}{x \left (x +1\right )} \end{align*}

✓ Maple. Time used: 0.114 (sec). Leaf size: 42

ode:=diff(y(x),x) = (x*y(x)+y(x)+x^4*(x^2+y(x)^2)^(1/2))/x/(1+x); 
dsolve(ode,y(x), singsol=all);
 

\[ \ln \left (y+\sqrt {y^{2}+x^{2}}\right )-\frac {x^{3}}{3}+\frac {x^{2}}{2}-x +\ln \left (x +1\right )-\ln \left (x \right )-c_{1} = 0 \]

✓ Mathematica. Time used: 0.217 (sec). Leaf size: 29

ode=D[y[x],x] == (y[x] + x*y[x] + x^4*Sqrt[x^2 + y[x]^2])/(x*(1 + x)); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x \sinh \left (\int _1^x\frac {K[1]^3}{K[1]+1}dK[1]+c_1\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (x**4*sqrt(x**2 + y(x)**2) + x*y(x) + y(x))/(x*(x + 1)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out