40.7.3 problem 20

Internal problem ID [8650]
Book : ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG, EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section : Chapter 6. Laplace Transforms. Problem set 6.3, page 224
Problem number : 20
Date solved : Tuesday, September 30, 2025 at 05:40:11 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+10 y^{\prime }+24 y&=144 t^{2} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&={\frac {19}{12}} \\ y^{\prime }\left (0\right )&=-5 \\ \end{align*}

✓ Maple. Time used: 0.093 (sec). Leaf size: 14

ode:=diff(diff(y(t),t),t)+10*diff(y(t),t)+24*y(t) = 144*t^2; 
ic:=[y(0) = 19/12, D(y)(0) = -5]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = 6 t^{2}-5 t +\frac {19}{12} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 17

ode=D[y[t],{t,2}]+10*D[y[t],t]+24*y[t]==144*t^2; 
ic={y[0]==19/12,Derivative[1][y][0] ==-5}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to 6 t^2-5 t+\frac {19}{12} \end{align*}

✓ Sympy. Time used: 0.130 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-144*t**2 + 24*y(t) + 10*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 19/12, Subs(Derivative(y(t), t), t, 0): -5} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 6 t^{2} - 5 t + \frac {19}{12} \]