20.10.5 problem Problem 18

Internal problem ID [3777]
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 18
Date solved : Tuesday, March 04, 2025 at 05:16:14 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=x^{4} \sin \left (x \right ) \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 17

ode:=x^2*diff(diff(y(x),x),x)-4*x*diff(y(x),x)+6*y(x) = x^4*sin(x); 
dsolve(ode,y(x), singsol=all);
 

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

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

ode=x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+6*y[x]==x^4*Sin[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x^2 (-\sin (x)+c_2 x+c_1) \]

✓ Sympy. Time used: 0.502 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**4*sin(x) + x**2*Derivative(y(x), (x, 2)) - 4*x*Derivative(y(x), x) + 6*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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