67.4.40 problem Problem 13(d)

Internal problem ID [14013]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 5.6 Laplace transform. Nonhomogeneous equations. Problems page 368
Problem number : Problem 13(d)
Date solved : Monday, March 31, 2025 at 08:21:50 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+y^{\prime }-y&=-t^{2}+2 t -10 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0 \end{align*}

✓ Maple. Time used: 0.098 (sec). Leaf size: 36

ode:=diff(diff(diff(y(t),t),t),t)-5*diff(diff(y(t),t),t)+diff(y(t),t)-y(t) = -t^2+2*t-10; 
ic:=y(0) = 2, D(y)(0) = 0, (D@@2)(y)(0) = 0; 
dsolve([ode,ic],y(t),method='laplace');
 

\[ y = \frac {\left (\munderset {\underline {\hspace {1.25 ex}}\alpha =\operatorname {RootOf}\left (\textit {\_Z}^{3}-5 \textit {\_Z}^{2}+\textit {\_Z} -1\right )}{\sum }\left (\underline {\hspace {1.25 ex}}\alpha -4\right ) \left (\underline {\hspace {1.25 ex}}\alpha -7\right ) {\mathrm e}^{\underline {\hspace {1.25 ex}}\alpha t}\right )}{26}+t^{2} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 1009

ode=D[ y[t],{t,3}]-5*D[y[t],{t,2}]+D[y[t],t]-y[t]==2*t-10-t^2; 
ic={y[0]==2,Derivative[1][y][0] ==0,Derivative[2][y][0] ==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t**2 - 2*t - y(t) + Derivative(y(t), t) - 5*Derivative(y(t), (t, 2)) + Derivative(y(t), (t, 3)) + 10,0) 
ics = {y(0): 2, Subs(Derivative(y(t), t), t, 0): 0, Subs(Derivative(y(t), (t, 2)), t, 0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

Timed Out