8.5.19 problem 19

Internal problem ID [747]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 19
Date solved : Saturday, March 29, 2025 at 10:18:19 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} 2 x y+x^{2} y^{\prime }&=5 y^{3} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 50

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

\begin{align*} y &= \frac {\sqrt {\left (c_1 \,x^{5}+2\right ) x}}{c_1 \,x^{5}+2} \\ y &= -\frac {\sqrt {\left (c_1 \,x^{5}+2\right ) x}}{c_1 \,x^{5}+2} \\ \end{align*}

✓ Mathematica. Time used: 0.505 (sec). Leaf size: 51

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

\begin{align*} y(x)\to -\frac {\sqrt {x}}{\sqrt {2+c_1 x^5}} \\ y(x)\to \frac {\sqrt {x}}{\sqrt {2+c_1 x^5}} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.561 (sec). Leaf size: 29

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

\[ \left [ y{\left (x \right )} = - \sqrt {\frac {x}{C_{1} x^{5} + 2}}, \ y{\left (x \right )} = \sqrt {\frac {x}{C_{1} x^{5} + 2}}\right ] \]