9.2.13 problem problem 25

Internal problem ID [947]
Book : Differential equations and linear algebra, 4th ed., Edwards and Penney
Section : Section 5.3, Higher-Order Linear Differential Equations. Homogeneous Equations with Constant Coefficients. Page 300
Problem number : problem 25
Date solved : Tuesday, March 04, 2025 at 12:06:18 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: 0.008 (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,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: 0.027 (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] ==-1,Derivative[2][y][0] ==3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{4} \left (14 x+27 e^{-2 x/3}-23\right ) \]

✓ Sympy. Time used: 0.100 (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)
 

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