89.11.29 problem 29

Internal problem ID [24554]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 8. Linear Differential Equations with constant coefficients. Exercises at page 117
Problem number : 29
Date solved : Thursday, October 02, 2025 at 10:46:05 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ y^{\prime }\left (0\right )&=-7 \\ y^{\prime \prime }\left (0\right )&=-1 \\ \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 17

ode:=diff(diff(diff(y(x),x),x),x)-2*diff(diff(y(x),x),x)-5*diff(y(x),x)+6*y(x) = 0; 
ic:=[y(0) = 1, D(y)(0) = -7, (D@@2)(y)(0) = -1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

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

ode=D[y[x],{x,3}] -2*D[y[x],{x,2}]-5*D[y[x],x] +6*y[x]==0; 
ic={y[0]==1,Derivative[1][y][0] ==-7,Derivative[2][y][0] ==-1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -e^{-2 x} \left (e^{5 x}-2\right ) \end{align*}

✓ Sympy. Time used: 0.117 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*y(x) - 5*Derivative(y(x), x) - 2*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {y(0): 1, Subs(Derivative(y(x), x), x, 0): -7, Subs(Derivative(y(x), (x, 2)), x, 0): -1} 
dsolve(ode,func=y(x),ics=ics)
 

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