70.13.8 problem 8

Internal problem ID [18877]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.3 (Linear homogeneous equations with constant coefficients). Problems at page 239
Problem number : 8
Date solved : Thursday, October 02, 2025 at 03:32:25 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 0.080 (sec). Leaf size: 14

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

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