88.23.11 problem 13

Internal problem ID [24185]
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. Miscellaneous Exercises at page 162
Problem number : 13
Date solved : Thursday, October 02, 2025 at 10:00:35 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+y&=x^{5}+2 x^{2} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 48

ode:=diff(diff(diff(y(x),x),x),x)-2*diff(diff(y(x),x),x)+y(x) = x^5+2*x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x^{5}+40 x^{3}-58 x^{2}+480 x -472+c_1 \,{\mathrm e}^{x}+c_2 \,{\mathrm e}^{-\frac {\left (\sqrt {5}-1\right ) x}{2}}+c_3 \,{\mathrm e}^{\frac {\left (\sqrt {5}+1\right ) x}{2}} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 63

ode=D[y[x],{x,3}]-2*D[y[x],{x,2}]+y[x]==x^5+2*x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x^5+40 x^3-58 x^2+480 x+c_1 e^{-\frac {1}{2} \left (\sqrt {5}-1\right ) x}+c_2 e^{\frac {1}{2} \left (1+\sqrt {5}\right ) x}+c_3 e^x-472 \end{align*}

✓ Sympy. Time used: 0.090 (sec). Leaf size: 53

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**5 - 2*x**2 + y(x) - 2*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{x} + C_{2} e^{\frac {x \left (1 - \sqrt {5}\right )}{2}} + C_{3} e^{\frac {x \left (1 + \sqrt {5}\right )}{2}} + x^{5} + 40 x^{3} - 58 x^{2} + 480 x - 472 \]