20.10.2 problem Problem 15

Internal problem ID [3774]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.8, A Differential Equation with Nonconstant Coefficients. page 567
Problem number : Problem 15
Date solved : Sunday, March 30, 2025 at 02:07:59 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y&=\cos \left (x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 17

ode:=x^2*diff(diff(y(x),x),x)+4*x*diff(y(x),x)+2*y(x) = cos(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_2 +c_1 x -\cos \left (x \right )}{x^{2}} \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 20

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

\[ y(x)\to \frac {-\cos (x)+c_2 x+c_1}{x^2} \]

✓ Sympy. Time used: 0.579 (sec). Leaf size: 14

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

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