14.1.14 problem 14

Internal problem ID [2485]
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 : 14
Date solved : Monday, January 27, 2025 at 05:54:03 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }-2 y t&=1 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 18

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

\[ y = \frac {\left (\sqrt {\pi }\, \operatorname {erf}\left (t \right )+2\right ) {\mathrm e}^{t^{2}}}{2} \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 24

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

\[ y(t)\to \frac {1}{2} e^{t^2} \left (\sqrt {\pi } \text {erf}(t)+2\right ) \]