51.3.12 problem 12

Internal problem ID [10355]
Book : First order enumerated odes
Section : section 3. First order odes solved using Laplace method
Problem number : 12
Date solved : Tuesday, September 30, 2025 at 07:22:32 PM
CAS classification : [_linear]

\begin{align*} \left (a t +1\right ) y^{\prime }+y&=t \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (1\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.139 (sec). Leaf size: 13

ode:=(a*t+1)*diff(y(t),t)+y(t) = t; 
ic:=[y(1) = 0]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = \frac {t -1}{a +1} \]

✓ Mathematica. Time used: 0.569 (sec). Leaf size: 14

ode=(1+a*t)*D[y[t],t]+y[t]==t; 
ic=y[1]==0; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {t-1}{a+1} \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
a = symbols("a") 
y = Function("y") 
ode = Eq(-t + (a*t + 1)*Derivative(y(t), t) + y(t),0) 
ics = {y(1): 0} 
dsolve(ode,func=y(t),ics=ics)