9.2.12 problem problem 24

Internal problem ID [946]
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 24
Date solved : Tuesday, March 04, 2025 at 12:06:17 PM
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: 0.010 (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,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.278 (sec). Leaf size: 70

ode=2*D[y[x],{x,3}]-3*D[y[x],{x,2}]-3*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]
 

\[ y(x)\to \frac {1}{66} e^{-\frac {1}{4} \left (\sqrt {33}-3\right ) x} \left (\left (99-13 \sqrt {33}\right ) e^{\frac {\sqrt {33} x}{2}}-132 e^{\frac {1}{4} \left (\sqrt {33}-3\right ) x}+99+13 \sqrt {33}\right ) \]

✓ Sympy. Time used: 0.222 (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)
 

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