7.10.37 problem 37

Internal problem ID [307]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.3 (Homogeneous equations with constant coefficients). Problems at page 134
Problem number : 37
Date solved : Tuesday, March 04, 2025 at 11:07:35 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }&=y^{\prime \prime \prime } \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=18\\ y^{\prime }\left (0\right )&=12\\ y^{\prime \prime }\left (0\right )&=13\\ y^{\prime \prime \prime }\left (0\right )&=7 \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 18

ode:=diff(diff(diff(diff(y(x),x),x),x),x) = diff(diff(diff(y(x),x),x),x); 
ic:=y(0) = 18, D(y)(0) = 12, (D@@2)(y)(0) = 13, (D@@3)(y)(0) = 7; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = 11+5 x +3 x^{2}+7 \,{\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 20

ode=D[y[x],{x,4}]==D[y[x],{x,3}]; 
ic={y[0]==18,Derivative[1][y][0] ==12,Derivative[2][y][0] ==13,Derivative[3][y][0] ==7}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to 3 x^2+5 x+7 e^x+11 \]

✓ Sympy. Time used: 0.100 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {y(0): 18, Subs(Derivative(y(x), x), x, 0): 12, Subs(Derivative(y(x), (x, 2)), x, 0): 13, Subs(Derivative(y(x), (x, 3)), x, 0): 7} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 3 x^{2} + 5 x + 7 e^{x} + 11 \]