1.4.21 problem 21

Internal problem ID [93]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.5 (linear equations). Problems at page 54
Problem number : 21
Date solved : Tuesday, September 30, 2025 at 03:43:06 AM
CAS classification : [_linear]

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

With initial conditions

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

✓ Maple. Time used: 0.027 (sec). Leaf size: 10

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

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

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 11

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

\begin{align*} y(x)&\to x^3 \sin (x) \end{align*}

✓ Sympy. Time used: 0.289 (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)
 

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