51.3.2 problem 2

Internal problem ID [10345]
Book : First order enumerated odes
Section : section 3. First order odes solved using Laplace method
Problem number : 2
Date solved : Tuesday, September 30, 2025 at 07:22:27 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }-t y&=0 \end{align*}

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.099 (sec). Leaf size: 5

ode:=diff(y(t),t)-t*y(t) = 0; 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = 0 \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 6

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

\begin{align*} y(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.149 (sec). Leaf size: 3

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

\[ y{\left (t \right )} = 0 \]