14.1.11 problem 11

Internal problem ID [2482]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.2. Linear equations. Excercises page 9
Problem number : 11
Date solved : Monday, January 27, 2025 at 05:53:56 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

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

dsolve([diff(y(t),t)-2*t*y(t)=t,y(0) = 1],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 18

DSolve[{D[y[t],t]-2*t*y[t]==t,{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
 

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