40.9.3 problem 13

Internal problem ID [6713]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 14. Linear equations with constant coefficients. Supplemetary problems. Page 92
Problem number : 13
Date solved : Wednesday, March 05, 2025 at 02:39:58 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }&=5 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

ode:=diff(diff(diff(y(x),x),x),x)-4*diff(diff(y(x),x),x) = 5; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{4 x} c_1}{16}-\frac {5 x^{2}}{8}+c_2 x +c_3 \]

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 30

ode=D[y[x],{x,3}]-4*D[y[x],{x,2}]==5; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {5 x^2}{8}+c_3 x+\frac {1}{16} c_1 e^{4 x}+c_2 \]

✓ Sympy. Time used: 0.111 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} e^{4 x} - \frac {5 x^{2}}{8} \]