88.20.8 problem 8

Internal problem ID [24146]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 5. Special Techniques for Linear Equations. Exercises at page 146
Problem number : 8
Date solved : Thursday, October 02, 2025 at 10:00:12 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+3 y&=-x^{6}+x^{4} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 37

ode:=diff(diff(y(x),x),x)+3*y(x) = -x^6+x^4; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sin \left (\sqrt {3}\, x \right ) c_2 +\cos \left (\sqrt {3}\, x \right ) c_1 -\frac {x^{6}}{3}+\frac {11 x^{4}}{3}-\frac {44 x^{2}}{3}+\frac {88}{9} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 49

ode=D[y[x],{x,2}]+3*y[x]==x^4-x^6; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{9} \left (-3 x^6+33 x^4-132 x^2+88\right )+c_1 \cos \left (\sqrt {3} x\right )+c_2 \sin \left (\sqrt {3} x\right ) \end{align*}

✓ Sympy. Time used: 0.072 (sec). Leaf size: 44

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**6 - x**4 + 3*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} \sin {\left (\sqrt {3} x \right )} + C_{2} \cos {\left (\sqrt {3} x \right )} - \frac {x^{6}}{3} + \frac {11 x^{4}}{3} - \frac {44 x^{2}}{3} + \frac {88}{9} \]