89.23.5 problem 5

Internal problem ID [24809]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 10. Nonhomogeneous Equations: Operational methods. Miscellaneous Exercises at page 162
Problem number : 5
Date solved : Thursday, October 02, 2025 at 10:48:12 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} 4 y+y^{\prime \prime }&=8 x^{5} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 30

ode:=diff(diff(y(x),x),x)+4*y(x) = 8*x^5; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sin \left (2 x \right ) c_2 +\cos \left (2 x \right ) c_1 +2 x^{5}-10 x^{3}+15 x \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 33

ode=D[y[x],{x,2}]+4*y[x]==8*x^5; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 2 x^5-10 x^3+15 x+c_1 \cos (2 x)+c_2 \sin (2 x) \end{align*}

✓ Sympy. Time used: 0.058 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-8*x**5 + 4*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} \sin {\left (2 x \right )} + C_{2} \cos {\left (2 x \right )} + 2 x^{5} - 10 x^{3} + 15 x \]