57.3.10 problem 10

Internal problem ID [9067]
Book : First order enumerated odes
Section : section 3. First order odes solved using Laplace method
Problem number : 10
Date solved : Monday, January 27, 2025 at 05:31:51 PM
CAS classification : [_linear]

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

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 1.438 (sec). Leaf size: 13

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

\[ y = \frac {1}{2 t}+\frac {t}{2} \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 17

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

\[ y(t)\to \frac {t^2+1}{2 t} \]