40.8.9 problem 24

Internal problem ID [6709]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 13. Homogeneous Linear equations with constant coefficients. Supplemetary problems. Page 86
Problem number : 24
Date solved : Sunday, March 30, 2025 at 11:20:19 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 20

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-6*diff(diff(diff(y(x),x),x),x)+13*diff(diff(y(x),x),x)-12*diff(y(x),x)+4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{x} \left (\left (c_2 x +c_1 \right ) {\mathrm e}^{x}+c_4 x +c_3 \right ) \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 29

ode=D[y[x],{x,4}]-6*D[y[x],{x,3}]+13*D[y[x],{x,2}]-12*D[y[x],x]+4*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^x \left (c_3 e^x+x \left (c_4 e^x+c_2\right )+c_1\right ) \]

✓ Sympy. Time used: 0.267 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*y(x) - 12*Derivative(y(x), x) + 13*Derivative(y(x), (x, 2)) - 6*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + C_{4} e^{x} + x \left (C_{2} + C_{3} e^{x}\right )\right ) e^{x} \]