56.21.1 problem Ex 1

Internal problem ID [14200]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VII, Linear differential equations with constant coefficients. Article 43. Page 92
Problem number : Ex 1
Date solved : Thursday, October 02, 2025 at 09:26:40 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 13

ode:=diff(diff(y(x),x),x)-3*diff(y(x),x)+2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{x} \left (c_1 \,{\mathrm e}^{x}+c_2 \right ) \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 18

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

\begin{align*} y(x)&\to e^x \left (c_2 e^x+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.085 (sec). Leaf size: 12

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

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