57.3.12 problem 12

Internal problem ID [9069]
Book : First order enumerated odes
Section : section 3. First order odes solved using Laplace method
Problem number : 12
Date solved : Monday, January 27, 2025 at 05:31:53 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*}

✓ Solution by Maple

Time used: 1.578 (sec). Leaf size: 13

dsolve([(1+a*t)*diff(y(t),t)+y(t)=t,y(1) = 0],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.599 (sec). Leaf size: 14

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

\[ y(t)\to \frac {t-1}{a+1} \]