15.10.20 problem 20

Internal problem ID [3107]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 18, page 82
Problem number : 20
Date solved : Sunday, March 30, 2025 at 01:18:36 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime \prime }-3 y^{\prime \prime }+11 y^{\prime }-40 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 34

ode:=2*diff(diff(diff(y(x),x),x),x)-3*diff(diff(y(x),x),x)+11*diff(y(x),x)-40*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{3 x}+c_2 \sin \left (\frac {\sqrt {31}\, x}{2}\right )+c_3 \cos \left (\frac {\sqrt {31}\, x}{2}\right )\right ) {\mathrm e}^{-\frac {x}{2}} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 50

ode=2*D[y[x],{x,3}]-3*D[y[x],{x,2}]+11*D[y[x],x]-40*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-x/2} \left (c_3 e^{3 x}+c_2 \cos \left (\frac {\sqrt {31} x}{2}\right )+c_1 \sin \left (\frac {\sqrt {31} x}{2}\right )\right ) \]

✓ Sympy. Time used: 0.242 (sec). Leaf size: 39

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-40*y(x) + 11*Derivative(y(x), x) - 3*Derivative(y(x), (x, 2)) + 2*Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{3} e^{\frac {5 x}{2}} + \left (C_{1} \sin {\left (\frac {\sqrt {31} x}{2} \right )} + C_{2} \cos {\left (\frac {\sqrt {31} x}{2} \right )}\right ) e^{- \frac {x}{2}} \]