67.9.12 problem 14.2 (b)

Internal problem ID [16560]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 14. Higher order equations and the reduction of order method. Additional exercises page 277
Problem number : 14.2 (b)
Date solved : Thursday, October 02, 2025 at 01:36:28 PM
CAS classification : [[_2nd_order, _missing_x]]

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

Using reduction of order method given that one solution is

\begin{align*} y&={\mathrm e}^{5 x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

ode:=diff(diff(y(x),x),x)-10*diff(y(x),x)+25*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{5 x} \left (c_2 x +c_1 \right ) \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 18

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

\begin{align*} y(x)&\to e^{5 x} (c_2 x+c_1) \end{align*}

✓ Sympy. Time used: 0.083 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = \left (C_{1} + C_{2} x\right ) e^{5 x} \]