84.27.4 problem 16.4

Internal problem ID [22277]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 16. Initial-value problems. Solved problems. Page 81
Problem number : 16.4
Date solved : Thursday, October 02, 2025 at 08:37:00 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (\pi \right )&=0 \\ y^{\prime }\left (\pi \right )&=0 \\ y^{\prime \prime }\left (\pi \right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.029 (sec). Leaf size: 33

ode:=diff(diff(diff(y(x),x),x),x)-6*diff(diff(y(x),x),x)+11*diff(y(x),x)-6*y(x) = 0; 
ic:=[y(Pi) = 0, D(y)(Pi) = 0, (D@@2)(y)(Pi) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{-3 \pi +3 x}}{2}-{\mathrm e}^{-2 \pi +2 x}+\frac {{\mathrm e}^{-\pi +x}}{2} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 27

ode=D[y[x],{x,3}]-6*D[y[x],{x,2}]+11*D[y[x],{x,1}]-6*y[x]==0; 
ic={y[Pi]==0,Derivative[1][y][Pi] ==0,Derivative[2][y][Pi] ==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} e^{x-3 \pi } \left (e^{\pi }-e^x\right )^2 \end{align*}

✓ Sympy. Time used: 0.126 (sec). Leaf size: 41

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*y(x) + 11*Derivative(y(x), x) - 6*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {y(pi): 0, Subs(Derivative(y(x), x), x, pi): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{3} e^{2 x} + C_{3} e^{2 \pi } + \left (- 2 C_{3} e^{\pi } + e^{- 2 \pi }\right ) e^{x} - e^{- \pi }\right ) e^{x} \]