8.3.14 problem 15

Internal problem ID [690]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.4. Separable equations. Page 43
Problem number : 15
Date solved : Saturday, March 29, 2025 at 10:13:39 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {\left (-1+x \right ) y^{5}}{x^{2} \left (-y+2 y^{3}\right )} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 840

ode:=diff(y(x),x) = (x-1)*y(x)^5/x^2/(-y(x)+2*y(x)^3); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 46.554 (sec). Leaf size: 842

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

\begin{align*} y(x)\to -\frac {\frac {8 \sqrt [3]{2} x^2}{\sqrt [3]{16 x^3-9 x^3 \log ^2(x)-9 c_1{}^2 x^3-18 c_1 x^2+3 \sqrt {x^2 (x \log (x)+c_1 x+1){}^2 \left (9 x^2 \log ^2(x)+\left (-32+9 c_1{}^2\right ) x^2+18 c_1 x+18 x (1+c_1 x) \log (x)+9\right )}-18 x^2 (1+c_1 x) \log (x)-9 x}}+2^{2/3} \sqrt [3]{16 x^3-9 x^3 \log ^2(x)-9 c_1{}^2 x^3-18 c_1 x^2+3 \sqrt {x^2 (x \log (x)+c_1 x+1){}^2 \left (9 x^2 \log ^2(x)+\left (-32+9 c_1{}^2\right ) x^2+18 c_1 x+18 x (1+c_1 x) \log (x)+9\right )}-18 x^2 (1+c_1 x) \log (x)-9 x}+4 x}{6 (x \log (x)+c_1 x+1)} \\ y(x)\to \frac {\frac {8 \sqrt [3]{2} \left (1+i \sqrt {3}\right ) x^2}{\sqrt [3]{16 x^3-9 x^3 \log ^2(x)-9 c_1{}^2 x^3-18 c_1 x^2+3 \sqrt {x^2 (x \log (x)+c_1 x+1){}^2 \left (9 x^2 \log ^2(x)+\left (-32+9 c_1{}^2\right ) x^2+18 c_1 x+18 x (1+c_1 x) \log (x)+9\right )}-18 x^2 (1+c_1 x) \log (x)-9 x}}+2^{2/3} \left (1-i \sqrt {3}\right ) \sqrt [3]{16 x^3-9 x^3 \log ^2(x)-9 c_1{}^2 x^3-18 c_1 x^2+3 \sqrt {x^2 (x \log (x)+c_1 x+1){}^2 \left (9 x^2 \log ^2(x)+\left (-32+9 c_1{}^2\right ) x^2+18 c_1 x+18 x (1+c_1 x) \log (x)+9\right )}-18 x^2 (1+c_1 x) \log (x)-9 x}-8 x}{12 (x \log (x)+c_1 x+1)} \\ y(x)\to \frac {\frac {8 \sqrt [3]{2} \left (1-i \sqrt {3}\right ) x^2}{\sqrt [3]{16 x^3-9 x^3 \log ^2(x)-9 c_1{}^2 x^3-18 c_1 x^2+3 \sqrt {x^2 (x \log (x)+c_1 x+1){}^2 \left (9 x^2 \log ^2(x)+\left (-32+9 c_1{}^2\right ) x^2+18 c_1 x+18 x (1+c_1 x) \log (x)+9\right )}-18 x^2 (1+c_1 x) \log (x)-9 x}}+2^{2/3} \left (1+i \sqrt {3}\right ) \sqrt [3]{16 x^3-9 x^3 \log ^2(x)-9 c_1{}^2 x^3-18 c_1 x^2+3 \sqrt {x^2 (x \log (x)+c_1 x+1){}^2 \left (9 x^2 \log ^2(x)+\left (-32+9 c_1{}^2\right ) x^2+18 c_1 x+18 x (1+c_1 x) \log (x)+9\right )}-18 x^2 (1+c_1 x) \log (x)-9 x}-8 x}{12 (x \log (x)+c_1 x+1)} \\ y(x)\to 0 \\ \end{align*}

✗ Sympy

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

Timed Out