6.18.19 problem section 9.2, problem 19

Internal problem ID [2133]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.2. constant coefficient. Page 483
Problem number : section 9.2, problem 19
Date solved : Tuesday, September 30, 2025 at 05:24:18 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 3 y^{\prime \prime \prime }-y^{\prime \prime }-7 y^{\prime }+5 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&={\frac {14}{5}} \\ y^{\prime }\left (0\right )&=0 \\ y^{\prime \prime }\left (0\right )&=10 \\ \end{align*}

✓ Maple. Time used: 0.049 (sec). Leaf size: 18

ode:=3*diff(diff(diff(y(x),x),x),x)-diff(diff(y(x),x),x)-7*diff(y(x),x)+5*y(x) = 0; 
ic:=[y(0) = 14/5, D(y)(0) = 0, (D@@2)(y)(0) = 10]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {9 \,{\mathrm e}^{-\frac {5 x}{3}}}{5}+{\mathrm e}^{x}+2 \,{\mathrm e}^{x} x \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 26

ode=3*D[y[x],{x,3}]-D[y[x],{x,2}]-7*D[y[x],x]+5*y[x]==0; 
ic={y[0]==14/5,Derivative[1][y][0] ==0,Derivative[2][y][0] ==10}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^x (2 x+1)+\frac {9}{5} e^{-5 x/3} \end{align*}

✓ Sympy. Time used: 0.142 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*y(x) - 7*Derivative(y(x), x) - Derivative(y(x), (x, 2)) + 3*Derivative(y(x), (x, 3)),0) 
ics = {y(0): 14/5, Subs(Derivative(y(x), x), x, 0): 0, Subs(Derivative(y(x), (x, 2)), x, 0): 10} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (2 x + 1\right ) e^{x} + \frac {9 e^{- \frac {5 x}{3}}}{5} \]