10.6.27 problem 27

Internal problem ID [1244]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Miscellaneous problems, end of chapter 2. Page 133
Problem number : 27
Date solved : Saturday, March 29, 2025 at 10:49:53 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Maple. Time used: 0.008 (sec). Leaf size: 35

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

\[ \frac {\left (-4 y^{3}-4 x^{2}-6 y^{2}-10 y-5\right ) {\mathrm e}^{-2 y}}{4}+c_1 = 0 \]

✓ Mathematica. Time used: 0.203 (sec). Leaf size: 48

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

\[ \text {Solve}\left [-\frac {1}{2} x^2 e^{-2 y(x)}-\frac {1}{8} e^{-2 y(x)} \left (4 y(x)^3+6 y(x)^2+10 y(x)+5\right )=c_1,y(x)\right ] \]

✓ Sympy. Time used: 1.002 (sec). Leaf size: 44

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x/(x**2 + y(x)**3 + y(x)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ C_{1} + \frac {x^{2} e^{- 2 y{\left (x \right )}}}{2} - \frac {\left (- 4 y^{3}{\left (x \right )} - 6 y^{2}{\left (x \right )} - 10 y{\left (x \right )} - 5\right ) e^{- 2 y{\left (x \right )}}}{8} = 0 \]