13.1.4 problem Example 6

Internal problem ID [2297]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.2. Page 6
Problem number : Example 6
Date solved : Monday, January 27, 2025 at 05:44:53 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }+2 y t&=t \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 17

dsolve([diff(y(t),t)+2*t*y(t)=t,y(1) = 2],y(t), singsol=all)
 

\[ y = \frac {1}{2}+\frac {3 \,{\mathrm e}^{-\left (-1+t \right ) \left (t +1\right )}}{2} \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 22

DSolve[{D[y[t],t]+2*t*y[t]==t,y[1]==2},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {3 e^{1-t^2}}{2}+\frac {1}{2} \]