46.6.10 problem 10

Internal problem ID [7356]
Book : ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG, EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section : Chapter 6. Laplace Transforms. Problem set 6.2, page 216
Problem number : 10
Date solved : Wednesday, March 05, 2025 at 04:23:56 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+\frac {y}{25}&=\frac {t^{2}}{50} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=-25\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Maple. Time used: 0.227 (sec). Leaf size: 11

ode:=diff(diff(y(t),t),t)+1/25*y(t) = 1/50*t^2; 
ic:=y(0) = -25, D(y)(0) = 0; 
dsolve([ode,ic],y(t),method='laplace');
 

\[ y = \frac {t^{2}}{2}-25 \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 14

ode=D[y[t],{t,2}]+4/100*y[t]==2/100*t^2; 
ic={y[0]==-25,Derivative[1][y][0] ==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {1}{2} \left (t^2-50\right ) \]

✓ Sympy. Time used: 0.121 (sec). Leaf size: 8

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t**2/50 + y(t)/25 + Derivative(y(t), (t, 2)),0) 
ics = {y(0): -25, Subs(Derivative(y(t), t), t, 0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {t^{2}}{2} - 25 \]