52.7.7 problem 17

Internal problem ID [8362]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 7 THE LAPLACE TRANSFORM. 7.4.1 DERIVATIVES OF A TRANSFORM. Page 309
Problem number : 17
Date solved : Wednesday, March 05, 2025 at 05:35:54 AM
CAS classification : [[_2nd_order, _missing_y]]

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

With initial conditions

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

✓ Maple. Time used: 0.011 (sec). Leaf size: 16

ode:=t*diff(diff(y(t),t),t)-diff(y(t),t) = 2*t^2; 
ic:=y(0) = 0; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = \frac {t^{2} \left (4 t +3 c_{1} \right )}{6} \]

✓ Mathematica. Time used: 0.057 (sec). Leaf size: 29

ode=D[y[t],{t,2}]-D[y[t],t]==2*t^2; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to -\frac {2 t^3}{3}-2 t^2-4 t+c_1 \left (e^t-1\right ) \]

✓ Sympy. Time used: 0.296 (sec). Leaf size: 14

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

\[ y{\left (t \right )} = C_{2} t^{2} + \frac {2 t^{3}}{3} \]