68.18.11 problem 17

Internal problem ID [17855]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 17
Date solved : Thursday, October 02, 2025 at 02:28:55 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime }-5 y^{\prime }+2 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=2*diff(diff(y(x),x),x)-5*diff(y(x),x)+2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 24

ode=2*D[y[x],{x,2}]-5*D[y[x],x]+2*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^{2 x} \end{align*}

✓ Sympy. Time used: 0.088 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*y(x) - 5*Derivative(y(x), x) + 2*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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