40.9.5 problem 15

Internal problem ID [6715]
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 : 15
Date solved : Wednesday, March 05, 2025 at 02:39:59 AM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 25

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

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

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 37

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

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

✓ Sympy. Time used: 0.238 (sec). Leaf size: 22

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

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