8.7.10 problem 10

Internal problem ID [816]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.1, second order linear equations. Page 299
Problem number : 10
Date solved : Saturday, March 29, 2025 at 10:31:24 PM
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: 0.045 (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,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.014 (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]
 

\[ y(x)\to e^{5 x} (3-2 x) \]

✓ Sympy. Time used: 0.173 (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)
 

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