1.10.25 problem 25

Internal problem ID [295]
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 2.3 (Homogeneous equations with constant coefficients). Problems at page 134
Problem number : 25
Date solved : Friday, October 17, 2025 at 04:22:00 PM
CAS classification : [[_3rd_order, _missing_x]]

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

With initial conditions

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

✓ Maple. Time used: 0.048 (sec). Leaf size: 15

ode:=3*diff(diff(diff(y(x),x),x),x)+2*diff(diff(y(x),x),x) = 0; 
ic:=[y(0) = -1, D(y)(0) = 0, (D@@2)(y)(0) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\frac {13}{4}+\frac {3 x}{2}+\frac {9 \,{\mathrm e}^{-\frac {2 x}{3}}}{4} \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 23

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

\begin{align*} y(x)&\to \frac {1}{4} \left (6 x+9 e^{-2 x/3}-13\right ) \end{align*}

✓ Sympy. Time used: 0.060 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = \frac {3 x}{2} - \frac {13}{4} + \frac {9 e^{- \frac {2 x}{3}}}{4} \]