51.3.14 problem 14

Internal problem ID [10357]
Book : First order enumerated odes
Section : section 3. First order odes solved using Laplace method
Problem number : 14
Date solved : Tuesday, September 30, 2025 at 07:22:33 PM
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 (-3\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.107 (sec). Leaf size: 5

ode:=diff(y(t),t)+(a*t+b*t)*y(t) = 0; 
ic:=[y(-3) = 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]+(a*t+b*t)*y[t]==0; 
ic=y[-3]==0; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.208 (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(-3): 0} 
dsolve(ode,func=y(t),ics=ics)
 

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