58.10.14 problem 14

Internal problem ID [14701]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients. Exercises page 135
Problem number : 14
Date solved : Thursday, October 02, 2025 at 09:50:20 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime \prime }+4 y^{\prime \prime }-7 y^{\prime }+2 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

ode:=4*diff(diff(diff(y(x),x),x),x)+4*diff(diff(y(x),x),x)-7*diff(y(x),x)+2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{\frac {x}{2}} \left (c_3 x +c_2 \right )+c_1 \,{\mathrm e}^{-2 x} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 93

ode=4*D[y[x],{x,3}]+4*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 c_1 \exp \left (x \text {Root}\left [4 \text {$\#$1}^3+4 \text {$\#$1}^2+7 \text {$\#$1}+2\&,1\right ]\right )+c_2 \exp \left (x \text {Root}\left [4 \text {$\#$1}^3+4 \text {$\#$1}^2+7 \text {$\#$1}+2\&,2\right ]\right )+c_3 \exp \left (x \text {Root}\left [4 \text {$\#$1}^3+4 \text {$\#$1}^2+7 \text {$\#$1}+2\&,3\right ]\right ) \end{align*}

✓ Sympy. Time used: 0.127 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*y(x) - 7*Derivative(y(x), x) + 4*Derivative(y(x), (x, 2)) + 4*Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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