13.1.3 problem Example 5

Internal problem ID [2296]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.2. Page 6
Problem number : Example 5
Date solved : Monday, January 27, 2025 at 05:44:53 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 12

dsolve(diff(y(t),t)-2*t*y(t)=t,y(t), singsol=all)
 

\[ y = -\frac {1}{2}+{\mathrm e}^{t^{2}} c_1 \]

✓ Solution by Mathematica

Time used: 0.051 (sec). Leaf size: 24

DSolve[D[y[t],t]-2*t*y[t]==t,y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to -\frac {1}{2}+c_1 e^{t^2} \\ y(t)\to -\frac {1}{2} \\ \end{align*}