35.8.22 problem 22

Internal problem ID [6229]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page 466
Problem number : 22
Date solved : Sunday, March 30, 2025 at 10:44:02 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+13 y^{\prime \prime }-18 y^{\prime }+36 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 37

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-2*diff(diff(diff(y(x),x),x),x)+13*diff(diff(y(x),x),x)-18*diff(y(x),x)+36*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{x} \sin \left (\sqrt {3}\, x \right )+c_2 \,{\mathrm e}^{x} \cos \left (\sqrt {3}\, x \right )+c_3 \sin \left (3 x \right )+c_4 \cos \left (3 x \right ) \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 48

ode=D[y[x],{x,4}]-2*D[y[x],{x,3}]+13*D[y[x],{x,2}]-18*D[y[x],x]+36*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_3 \cos (3 x)+c_2 e^x \cos \left (\sqrt {3} x\right )+c_4 \sin (3 x)+c_1 e^x \sin \left (\sqrt {3} x\right ) \]

✓ Sympy. Time used: 0.247 (sec). Leaf size: 39

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(36*y(x) - 18*Derivative(y(x), x) + 13*Derivative(y(x), (x, 2)) - 2*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{3} \sin {\left (3 x \right )} + C_{4} \cos {\left (3 x \right )} + \left (C_{1} \sin {\left (\sqrt {3} x \right )} + C_{2} \cos {\left (\sqrt {3} x \right )}\right ) e^{x} \]