12.5.11 problem 7

Internal problem ID [1635]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable Equations. Section 2.4 Page 68
Problem number : 7
Date solved : Saturday, March 29, 2025 at 11:08:57 PM
CAS classification : [_Bernoulli]

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

With initial conditions

\begin{align*} y \left (0\right )&=2 \sqrt {2} \end{align*}

✓ Maple. Time used: 0.052 (sec). Leaf size: 13

ode:=diff(y(x),x)-2*y(x) = x*y(x)^3; 
ic:=y(0) = 2*2^(1/2); 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {4}{\sqrt {-8 x +2}} \]

✓ Mathematica. Time used: 1.839 (sec). Leaf size: 34

ode=D[y[x],x]-2*y[x]==x*y[x]^3; 
ic=y[0]==2*Sqrt[2]; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {2 i \sqrt {2} e^{2 x}}{\sqrt {e^{4 x} (4 x-1)}} \]

✓ Sympy. Time used: 1.338 (sec). Leaf size: 31

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

\[ y{\left (x \right )} = 2 \sqrt {2} \sqrt {\frac {e^{4 x}}{- 4 x e^{4 x} + e^{4 x}}} \]