46.7.7 problem 17

Internal problem ID [9648]
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 : Tuesday, September 30, 2025 at 06:21:51 PM
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: 0.025 (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,op(ic)],y(t), singsol=all);
 

\[ y = \frac {t^{2} \left (4 t +3 c_1 \right )}{6} \]

✓ Mathematica. Time used: 0.053 (sec). Leaf size: 44

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]
 

\begin{align*} y(t)&\to e^t \int _0^t2 e^{-K[1]} K[1]^2dK[1]-\frac {2 t^3}{3}+c_1 \left (e^t-1\right ) \end{align*}

✓ Sympy. Time used: 0.184 (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)
 

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