1.10.24 problem 24

Internal problem ID [294]
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 : 24
Date solved : Tuesday, September 30, 2025 at 03:54:39 AM
CAS classification : [[_3rd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ y^{\prime }\left (0\right )&=-1 \\ y^{\prime \prime }\left (0\right )&=3 \\ \end{align*}

✓ Maple. Time used: 0.046 (sec). Leaf size: 18

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

\[ y = -\frac {7}{2}+4 \,{\mathrm e}^{-\frac {x}{2}}+\frac {{\mathrm e}^{2 x}}{2} \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 25

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

\begin{align*} y(x)&\to \frac {1}{2} \left (8 e^{-x/2}+e^{2 x}-7\right ) \end{align*}

✓ Sympy. Time used: 0.131 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = \frac {e^{2 x}}{2} - \frac {7}{2} + 4 e^{- \frac {x}{2}} \]