83.11.2 problem 2

Internal problem ID [21991]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter VI. Linear equations with constant coefficients. Ex. XIII at page 106
Problem number : 2
Date solved : Thursday, October 02, 2025 at 08:21:29 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 +c_2 \,{\mathrm e}^{2 x} \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 19

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

\begin{align*} y(x)&\to \frac {1}{2} c_1 e^{2 x}+c_2 \end{align*}

✓ Sympy. Time used: 0.072 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = C_{1} + C_{2} e^{2 x} \]