15.9.23 problem 37

Internal problem ID [3080]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 17, page 78
Problem number : 37
Date solved : Sunday, March 30, 2025 at 01:18:06 AM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 33

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

\[ y = c_1 \,{\mathrm e}^{\frac {x}{2}}+c_2 \,{\mathrm e}^{\frac {\left (\sqrt {3}-1\right ) x}{2}}+c_3 \,{\mathrm e}^{-\frac {\left (1+\sqrt {3}\right ) x}{2}} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 50

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

\[ y(x)\to c_1 e^{-\frac {1}{2} \left (1+\sqrt {3}\right ) x}+c_2 e^{\frac {1}{2} \left (\sqrt {3}-1\right ) x}+c_3 e^{x/2} \]

✓ Sympy. Time used: 0.242 (sec). Leaf size: 41

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

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