15.22.3 problem 3

Internal problem ID [3337]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 40, page 186
Problem number : 3
Date solved : Tuesday, March 04, 2025 at 04:36:22 PM
CAS classification : [_separable]

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

Using series method with expansion around

\begin{align*} 1 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 5

Order:=5; 
ode:=diff(y(x),x) = x^2*y(x)^2; 
ic:=y(1) = 0; 
dsolve([ode,ic],y(x),type='series',x=1);
 

\[ y \left (x \right ) = 0 \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 4

ode=D[y[x],x]==x^2*y[x]^2; 
ic={y[1]==0}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,1,4}]
 

\[ y(x)\to 0 \]

✓ Sympy. Time used: 0.681 (sec). Leaf size: 5

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2*y(x)**2 + Derivative(y(x), x),0) 
ics = {y(1): 0} 
dsolve(ode,func=y(x),ics=ics,hint="1st_power_series",x0=1,n=5)
 

\[ y{\left (x \right )} = O\left (x^{5}\right ) \]