1.4.18 problem 18

Internal problem ID [90]
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 : 18
Date solved : Tuesday, September 30, 2025 at 03:43:01 AM
CAS classification : [_linear]

\begin{align*} x y^{\prime }&=2 y+x^{3} \cos \left (x \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

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

\[ y = \left (\sin \left (x \right )+c_1 \right ) x^{2} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 14

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

\begin{align*} y(x)&\to x^2 (\sin (x)+c_1) \end{align*}

✓ Sympy. Time used: 0.226 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = x^{2} \left (C_{1} + \sin {\left (x \right )}\right ) \]