15.10.22 problem 22

Internal problem ID [3109]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 18, page 82
Problem number : 22
Date solved : Sunday, March 30, 2025 at 01:18:38 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime \prime }+12 y^{\prime \prime }-3 y^{\prime }+14 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 37

ode:=4*diff(diff(diff(y(x),x),x),x)+12*diff(diff(y(x),x),x)-3*diff(y(x),x)+14*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{-\frac {7 x}{2}}+c_2 \,{\mathrm e}^{\frac {x}{4}} \sin \left (\frac {\sqrt {15}\, x}{4}\right )+c_3 \,{\mathrm e}^{\frac {x}{4}} \cos \left (\frac {\sqrt {15}\, x}{4}\right ) \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 58

ode=4*D[y[x],{x,3}]+12*D[y[x],{x,2}]-3*D[y[x],x]+14*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_3 e^{-7 x/2}+c_2 e^{x/4} \cos \left (\frac {\sqrt {15} x}{4}\right )+c_1 e^{x/4} \sin \left (\frac {\sqrt {15} x}{4}\right ) \]

✓ Sympy. Time used: 0.251 (sec). Leaf size: 39

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(14*y(x) - 3*Derivative(y(x), x) + 12*Derivative(y(x), (x, 2)) + 4*Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{3} e^{- \frac {7 x}{2}} + \left (C_{1} \sin {\left (\frac {\sqrt {15} x}{4} \right )} + C_{2} \cos {\left (\frac {\sqrt {15} x}{4} \right )}\right ) e^{\frac {x}{4}} \]