78.16.21 problem 21

Internal problem ID [18329]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 23. Operator Methods for Finding Particular Solutions. Problems at page 169
Problem number : 21
Date solved : Monday, March 31, 2025 at 05:25:43 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 25

ode:=diff(diff(diff(y(x),x),x),x)-1/4*diff(y(x),x) = x; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.041 (sec). Leaf size: 35

ode=D[y[x],{x,3}]-1/4*D[y[x],x]==x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.164 (sec). Leaf size: 22

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

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