20.12.5 problem Problem 20

Internal problem ID [3799]
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 8.10, Chapter review. page 575
Problem number : Problem 20
Date solved : Sunday, March 30, 2025 at 02:08:48 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+25 y^{\prime }&=x^{2} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 49

ode:=diff(diff(diff(y(x),x),x),x)-6*diff(diff(y(x),x),x)+25*diff(y(x),x) = x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (\left (3 c_1 -4 c_2 \right ) \cos \left (4 x \right )+4 \sin \left (4 x \right ) \left (c_1 +\frac {3 c_2}{4}\right )\right ) {\mathrm e}^{3 x}}{25}+\frac {x^{3}}{75}+\frac {6 x^{2}}{625}+\frac {22 x}{15625}+c_3 \]

✓ Mathematica. Time used: 0.274 (sec). Leaf size: 71

ode=D[y[x],{x,3}]-6*D[y[x],{x,2}]+25*D[y[x],x]==x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {x^3}{75}+\frac {6 x^2}{625}+\frac {22 x}{15625}-\frac {1}{25} (4 c_1-3 c_2) e^{3 x} \cos (4 x)+\frac {1}{25} (3 c_1+4 c_2) e^{3 x} \sin (4 x)+c_3 \]

✓ Sympy. Time used: 0.226 (sec). Leaf size: 39

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2 + 25*Derivative(y(x), x) - 6*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + \frac {x^{3}}{75} + \frac {6 x^{2}}{625} + \frac {22 x}{15625} + \left (C_{2} \sin {\left (4 x \right )} + C_{3} \cos {\left (4 x \right )}\right ) e^{3 x} \]