60.2.285 problem 863

Internal problem ID [10859]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 863
Date solved : Sunday, March 30, 2025 at 07:16:29 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} y^{\prime }&=\frac {y+x \sqrt {y^{2}+x^{2}}+x^{3} \sqrt {y^{2}+x^{2}}+x^{4} \sqrt {y^{2}+x^{2}}}{x} \end{align*}

✓ Maple. Time used: 17.844 (sec). Leaf size: 38

ode:=diff(y(x),x) = (y(x)+x*(x^2+y(x)^2)^(1/2)+x^3*(x^2+y(x)^2)^(1/2)+x^4*(x^2+y(x)^2)^(1/2))/x; 
dsolve(ode,y(x), singsol=all);
 

\[ \ln \left (y+\sqrt {y^{2}+x^{2}}\right )-\frac {x^{4}}{4}-\frac {x^{3}}{3}-x -\ln \left (x \right )-c_{1} = 0 \]

✓ Mathematica. Time used: 0.378 (sec). Leaf size: 26

ode=D[y[x],x] == (y[x] + x*Sqrt[x^2 + y[x]^2] + x^3*Sqrt[x^2 + y[x]^2] + x^4*Sqrt[x^2 + y[x]^2])/x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x \sinh \left (\frac {x^4}{4}+\frac {x^3}{3}+x+c_1\right ) \]

✗ 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**3*sqrt(x**2 + y(x)**2) + x*sqrt(x**2 + y(x)**2) + y(x))/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out