57.3.13 problem 13

Internal problem ID [9070]
Book : First order enumerated odes
Section : section 3. First order odes solved using Laplace method
Problem number : 13
Date solved : Wednesday, March 05, 2025 at 07:19:00 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }+\left (a t +b t \right ) y&=0 \end{align*}

Using Laplace method With initial conditions

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

✓ Maple. Time used: 1.399 (sec). Leaf size: 5

ode:=diff(y(t),t)+(a*t+b*t)*y(t) = 0; 
ic:=y(0) = 0; 
dsolve([ode,ic],y(t),method='laplace');
 

\[ y = 0 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 6

ode=D[y[t],t]+(a*t+b*t)*y[t]==0; 
ic=y[0]==0; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to 0 \]

✓ Sympy. Time used: 0.340 (sec). Leaf size: 3

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

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