89.12.28 problem 28

Internal problem ID [24582]
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 121
Problem number : 28
Date solved : Thursday, October 02, 2025 at 10:46:14 PM
CAS classification : [[_3rd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=-3 \\ y^{\prime }\left (0\right )&=0 \\ y^{\prime \prime }\left (0\right )&=12 \\ \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 15

ode:=diff(diff(diff(y(x),x),x),x)+2*diff(diff(y(x),x),x) = 0; 
ic:=[y(0) = -3, D(y)(0) = 0, (D@@2)(y)(0) = 12]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -6+6 x +3 \,{\mathrm e}^{-2 x} \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 17

ode=D[y[x],{x,3}]+2*D[y[x],{x,2}] ==0; 
ic={y[0]==-3,Derivative[1][y][0] ==0,Derivative[2][y][0] ==12}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 6 x+3 e^{-2 x}-6 \end{align*}

✓ Sympy. Time used: 0.053 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {y(0): -3, Subs(Derivative(y(x), x), x, 0): 0, Subs(Derivative(y(x), (x, 2)), x, 0): 12} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 6 x - 6 + 3 e^{- 2 x} \]