64.8.5 problem 8

Internal problem ID [13314]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.1. Basic theory of linear differential equations. Exercises page 113
Problem number : 8
Date solved : Wednesday, March 05, 2025 at 09:47:52 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=4 \end{align*}

✓ Maple. Time used: 0.015 (sec). Leaf size: 12

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x)+y(x) = 0; 
ic:=y(0) = 1, D(y)(0) = 4; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = {\mathrm e}^{x} \left (3 x +1\right ) \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 14

ode=D[y[x],{x,2}]-2*D[y[x],x]+y[x]==0; 
ic={y[0]==1,Derivative[1][y][0] ==4}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^x (3 x+1) \]

✓ Sympy. Time used: 0.150 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) - 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 1, Subs(Derivative(y(x), x), x, 0): 4} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (3 x + 1\right ) e^{x} \]