85.37.4 problem 1 (d)

Internal problem ID [22747]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 175
Problem number : 1 (d)
Date solved : Thursday, October 02, 2025 at 09:14:18 PM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 18

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

\[ y = c_1 +c_2 \,{\mathrm e}^{2 x}+c_3 \,{\mathrm e}^{\frac {x}{2}} \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 30

ode=2*D[y[x],{x,3}]-5*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 2 c_1 e^{x/2}+\frac {1}{2} c_2 e^{2 x}+c_3 \end{align*}

✓ Sympy. Time used: 0.103 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*Derivative(y(x), x) - 5*Derivative(y(x), (x, 2)) + 2*Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} e^{\frac {x}{2}} + C_{3} e^{2 x} \]