54.2.355 problem 934

Internal problem ID [12229]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 934
Date solved : Wednesday, October 01, 2025 at 01:15:16 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Abel]

\begin{align*} y^{\prime }&=\frac {x}{2}+1+y^{2}+\frac {x^{2} y}{4}-x y-\frac {x^{4}}{8}+\frac {x^{3}}{8}+\frac {x^{2}}{4}+y^{3}-\frac {3 x^{2} y^{2}}{4}-\frac {3 x y^{2}}{2}+\frac {3 y x^{4}}{16}+\frac {3 x^{3} y}{4}-\frac {x^{6}}{64}-\frac {3 x^{5}}{32} \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 39

ode:=diff(y(x),x) = 1/2*x+1+y(x)^2+1/4*x^2*y(x)-x*y(x)-1/8*x^4+1/8*x^3+1/4*x^2+y(x)^3-3/4*x^2*y(x)^2-3/2*x*y(x)^2+3/16*y(x)*x^4+3/4*x^3*y(x)-1/64*x^6-3/32*x^5; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{2}}{4}+\frac {x}{2}+\operatorname {RootOf}\left (-x +2 \int _{}^{\textit {\_Z}}\frac {1}{2 \textit {\_a}^{3}+2 \textit {\_a}^{2}+1}d \textit {\_a} +c_1 \right ) \]

✓ Mathematica. Time used: 0.13 (sec). Leaf size: 71

ode=D[y[x],x] == 1 + x/2 + x^2/4 + x^3/8 - x^4/8 - (3*x^5)/32 - x^6/64 - x*y[x] + (x^2*y[x])/4 + (3*x^3*y[x])/4 + (3*x^4*y[x])/16 + y[x]^2 - (3*x*y[x]^2)/2 - (3*x^2*y[x]^2)/4 + y[x]^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{\sqrt [3]{\frac {2}{31}} \left (\frac {1}{4} \left (-3 x^2-6 x+4\right )+3 y(x)\right )}\frac {1}{K[1]^3-3 \left (\frac {2}{31}\right )^{2/3} K[1]+1}dK[1]=\frac {1}{9} \left (\frac {31}{2}\right )^{2/3} x+c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**6/64 + 3*x**5/32 - 3*x**4*y(x)/16 + x**4/8 - 3*x**3*y(x)/4 - x**3/8 + 3*x**2*y(x)**2/4 - x**2*y(x)/4 - x**2/4 + 3*x*y(x)**2/2 + x*y(x) - x/2 - y(x)**3 - y(x)**2 + Derivative(y(x), x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out