8.4.21 problem 21

Internal problem ID [724]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.5. Linear first order equations. Page 56
Problem number : 21
Date solved : Tuesday, March 04, 2025 at 11:34:15 AM
CAS classification : [_linear]

\begin{align*} x y^{\prime }&=x^{4} \cos \left (x \right )+3 y \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.012 (sec). Leaf size: 10

ode:=x*diff(y(x),x) = x^4*cos(x)+3*y(x); 
ic:=y(2*Pi) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \sin \left (x \right ) x^{3} \]

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 11

ode=x*D[y[x],x] == x^4*Cos[x]+3*y[x]; 
ic=y[2*Pi]==0; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x^3 \sin (x) \]

✓ Sympy. Time used: 0.426 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**4*cos(x) + x*Derivative(y(x), x) - 3*y(x),0) 
ics = {y(2*pi): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x^{3} \sin {\left (x \right )} \]