88.22.12 problem 16

Internal problem ID [24172]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 5. Special Techniques for Linear Equations. Exercises at page 160 (Laplace transform)
Problem number : 16
Date solved : Thursday, October 02, 2025 at 10:00:26 PM
CAS classification : [[_high_order, _quadrature]]

\begin{align*} y^{\left (5\right )}&=120 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=0 \\ y^{\prime }\left (0\right )&=0 \\ y^{\prime \prime }\left (0\right )&=0 \\ y^{\prime \prime \prime }\left (0\right )&=6 \\ y^{\prime \prime \prime \prime }\left (0\right )&=24 \\ \end{align*}

✓ Maple. Time used: 0.039 (sec). Leaf size: 14

ode:=diff(diff(diff(diff(diff(y(x),x),x),x),x),x) = 120; 
ic:=[y(0) = 0, D(y)(0) = 0, (D@@2)(y)(0) = 0, (D@@3)(y)(0) = 6, (D@@4)(y)(0) = 24]; 
dsolve([ode,op(ic)],y(x),method='laplace');
 

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 15

ode=D[y[x],{x,5}]==120; 
ic={y[0]==0,Derivative[1][y][0] ==0,Derivative[2][y][0] ==0,Derivative[3][y][0] ==6,Derivative[4][y][0] ==24}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x^3 \left (x^2+x+1\right ) \end{align*}

✓ Sympy. Time used: 0.095 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), (x, 5)) - 120,0) 
ics = {y(0): 0, Subs(Derivative(y(x), x), x, 0): 0, Subs(Derivative(y(x), (x, 2)), x, 0): 0, Subs(Derivative(y(x), (x, 3)), x, 0): 6, Subs(Derivative(y(x), (x, 4)), x, 0): 24} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x^{5} + x^{4} + x^{3} \]