33.5.12 problem Problem 24.35

Internal problem ID [7841]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 24. Solutions of linear DE by Laplace transforms. Supplementary Problems. page 248
Problem number : Problem 24.35
Date solved : Tuesday, September 30, 2025 at 05:06:14 PM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Maple. Time used: 0.092 (sec). Leaf size: 23

ode:=diff(diff(diff(y(x),x),x),x)-y(x) = 5; 
ic:=[y(0) = 0, D(y)(0) = 0, (D@@2)(y)(0) = 0]; 
dsolve([ode,op(ic)],y(x),method='laplace');
 

\[ y = \frac {5 \,{\mathrm e}^{x}}{3}-5+\frac {10 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )}{3} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 34

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

\begin{align*} y(x)&\to \frac {5}{3} \left (e^x+2 e^{-x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )-3\right ) \end{align*}

✓ Sympy. Time used: 0.128 (sec). Leaf size: 29

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

\[ y{\left (x \right )} = \frac {5 e^{x}}{3} - 5 + \frac {10 e^{- \frac {x}{2}} \cos {\left (\frac {\sqrt {3} x}{2} \right )}}{3} \]