89.11.13 problem 13

Internal problem ID [24538]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 8. Linear Differential Equations with constant coefficients. Exercises at page 117
Problem number : 13
Date solved : Thursday, October 02, 2025 at 10:45:58 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 10 y^{\prime \prime \prime }+y^{\prime \prime }-7 y^{\prime }+2 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

ode:=10*diff(diff(diff(y(x),x),x),x)+diff(diff(y(x),x),x)-7*diff(y(x),x)+2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{\frac {x}{2}}+c_2 \,{\mathrm e}^{-x}+c_3 \,{\mathrm e}^{\frac {2 x}{5}} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 34

ode=10*D[y[x],{x,3}] +D[y[x],{x,2}]-7*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_1 e^{7 x/5}+c_2 e^{3 x/2}+c_3\right ) \end{align*}

✓ Sympy. Time used: 0.099 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*y(x) - 7*Derivative(y(x), x) + Derivative(y(x), (x, 2)) + 10*Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- x} + C_{2} e^{\frac {2 x}{5}} + C_{3} e^{\frac {x}{2}} \]