6.8.1 problem 1

Internal problem ID [1737]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 5 linear second order equations. Section 5.1 Homogeneous linear equations. Page 203
Problem number : 1
Date solved : Tuesday, September 30, 2025 at 05:18:50 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-7 y^{\prime }+10 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-1 \\ y^{\prime }\left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.059 (sec). Leaf size: 15

ode:=diff(diff(y(x),x),x)-7*diff(y(x),x)+10*y(x) = 0; 
ic:=[y(0) = -1, D(y)(0) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = {\mathrm e}^{5 x}-2 \,{\mathrm e}^{2 x} \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 18

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

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

✓ Sympy. Time used: 0.136 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(10*y(x) - 7*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): -1, Subs(Derivative(y(x), x), x, 0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

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