1.9.2 problem 14

Internal problem ID [250]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.2 (General solutions of linear equations). Problems at page 122
Problem number : 14
Date solved : Tuesday, September 30, 2025 at 03:54:14 AM
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 (0\right )&=0 \\ y^{\prime }\left (0\right )&=0 \\ y^{\prime \prime }\left (0\right )&=3 \\ \end{align*}

✓ Maple. Time used: 0.047 (sec). Leaf size: 14

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(0) = 0, D(y)(0) = 0, (D@@2)(y)(0) = 3]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {3 \,{\mathrm e}^{x} \left ({\mathrm e}^{x}-1\right )^{2}}{2} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 19

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

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

✓ Sympy. Time used: 0.135 (sec). Leaf size: 22

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(0): 0, Subs(Derivative(y(x), x), x, 0): 0, Subs(Derivative(y(x), (x, 2)), x, 0): 3} 
dsolve(ode,func=y(x),ics=ics)
 

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