40.8.4 problem 19

Internal problem ID [6704]
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 : 19
Date solved : Sunday, March 30, 2025 at 11:20:13 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+12 y^{\prime \prime }-8 y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-6*diff(diff(diff(y(x),x),x),x)+12*diff(diff(y(x),x),x)-8*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_4 \,x^{2}+c_3 x +c_2 \right ) {\mathrm e}^{2 x}+c_1 \]

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 43

ode=D[y[x],{x,4}]-6*D[y[x],{x,3}]+12*D[y[x],{x,2}]-8*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{4} e^{2 x} \left (c_3 \left (2 x^2-2 x+1\right )+c_2 (2 x-1)+2 c_1\right )+c_4 \]

✓ Sympy. Time used: 0.220 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-8*Derivative(y(x), x) + 12*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)
 

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