58.8.5 problem 8

Internal problem ID [14674]
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 : Thursday, October 02, 2025 at 09:50:05 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

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

✓ Maple. Time used: 0.038 (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,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.008 (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]
 

\begin{align*} y(x)&\to e^x (3 x+1) \end{align*}

✓ Sympy. Time used: 0.087 (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)
 

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