67.2.26 problem Problem 3(d)

Internal problem ID [13912]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 3(d)
Date solved : Monday, March 31, 2025 at 08:17:51 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 3 y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 38

ode:=3*diff(diff(diff(diff(y(x),x),x),x),x)-2*diff(diff(y(x),x),x)+diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 +c_2 \,{\mathrm e}^{-x}+c_3 \,{\mathrm e}^{\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{6}\right )+c_4 \,{\mathrm e}^{\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{6}\right ) \]

✓ Mathematica. Time used: 0.368 (sec). Leaf size: 71

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

\[ y(x)\to \int _1^x\left (e^{-K[1]} c_3+e^{\frac {K[1]}{2}} c_2 \cos \left (\frac {K[1]}{2 \sqrt {3}}\right )+e^{\frac {K[1]}{2}} c_1 \sin \left (\frac {K[1]}{2 \sqrt {3}}\right )\right )dK[1]+c_4 \]

✓ Sympy. Time used: 0.189 (sec). Leaf size: 37

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

\[ y{\left (x \right )} = C_{1} + C_{4} e^{- x} + \left (C_{2} \sin {\left (\frac {\sqrt {3} x}{6} \right )} + C_{3} \cos {\left (\frac {\sqrt {3} x}{6} \right )}\right ) e^{\frac {x}{2}} \]