1.10.26 problem 26

Internal problem ID [296]
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 : 26
Date solved : Tuesday, September 30, 2025 at 03:54:40 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+10 y^{\prime \prime }+25 y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3 \\ y^{\prime }\left (0\right )&=4 \\ y^{\prime \prime }\left (0\right )&=5 \\ \end{align*}

✓ Maple. Time used: 0.040 (sec). Leaf size: 19

ode:=diff(diff(diff(y(x),x),x),x)+10*diff(diff(y(x),x),x)+25*diff(y(x),x) = 0; 
ic:=[y(0) = 3, D(y)(0) = 4, (D@@2)(y)(0) = 5]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {24}{5}-\frac {9 \,{\mathrm e}^{-5 x}}{5}-5 \,{\mathrm e}^{-5 x} x \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 26

ode=D[y[x],{x,3}]+10*D[y[x],{x,2}]+25*D[y[x],x]==0; 
ic={y[0]==3,Derivative[1][y][0] ==4,Derivative[2][y][0] ==5}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{5} e^{-5 x} \left (-25 x+24 e^{5 x}-9\right ) \end{align*}

✓ Sympy. Time used: 0.130 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(25*Derivative(y(x), x) + 10*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {y(0): 3, Subs(Derivative(y(x), x), x, 0): 4, Subs(Derivative(y(x), (x, 2)), x, 0): 5} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (- 5 x - \frac {9}{5}\right ) e^{- 5 x} + \frac {24}{5} \]