15.9.21 problem 35

Internal problem ID [3078]
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 : 35
Date solved : Sunday, March 30, 2025 at 01:18:04 AM
CAS classification : [[_high_order, _missing_x]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 24

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

\[ y = c_1 +c_2 \,{\mathrm e}^{-\frac {x}{2}}+c_3 \,{\mathrm e}^{\frac {x}{2}}+c_4 \,{\mathrm e}^{\frac {x}{3}} \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 39

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

\[ y(x)\to e^{-x/2} \left (3 c_1 e^{5 x/6}+2 c_3 e^x-2 c_2\right )+c_4 \]

✓ Sympy. Time used: 0.158 (sec). Leaf size: 24

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

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