23.2.11 problem 5

Internal problem ID [4128]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 3. Linear differential equations of second order. Exercises at page 31
Problem number : 5
Date solved : Sunday, March 30, 2025 at 02:40:32 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+5 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=7 \end{align*}

✓ Maple. Time used: 0.051 (sec). Leaf size: 13

ode:=diff(diff(y(x),x),x)-6*diff(y(x),x)+5*y(x) = 0; 
ic:=y(0) = 3, D(y)(0) = 7; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 16

ode=D[y[x],{x,2}]-6*D[y[x],x]+5*y[x]==0; 
ic={y[0]==3,Derivative[1][y][0] ==7}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^x \left (e^{4 x}+2\right ) \]

✓ Sympy. Time used: 0.147 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*y(x) - 6*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 3, Subs(Derivative(y(x), x), x, 0): 7} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (e^{4 x} + 2\right ) e^{x} \]