1.8.10 problem 10

Internal problem ID [224]
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 2.1 (Introduction. Second order linear equations). Problems at page 111
Problem number : 10
Date solved : Tuesday, September 30, 2025 at 03:53:53 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=3 \\ y^{\prime }\left (0\right )&=13 \\ \end{align*}

✓ Maple. Time used: 0.052 (sec). Leaf size: 14

ode:=diff(diff(y(x),x),x)-10*diff(y(x),x)+25*y(x) = 0; 
ic:=[y(0) = 3, D(y)(0) = 13]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = {\mathrm e}^{5 x} \left (3-2 x \right ) \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 16

ode=D[y[x],{x,2}]-10*D[y[x],x]+25*y[x] == 0; 
ic={y[0]==3,Derivative[1][y][0] ==13}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{5 x} (3-2 x) \end{align*}

✓ Sympy. Time used: 0.099 (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 = {y(0): 3, Subs(Derivative(y(x), x), x, 0): 13} 
dsolve(ode,func=y(x),ics=ics)
 

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