13.2.13 problem 14

Internal problem ID [2311]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.2. Page 9
Problem number : 14
Date solved : Monday, January 27, 2025 at 05:45:21 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: 0.010 (sec). Leaf size: 18

dsolve([-2*t*y(t)+diff(y(t),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: 0.038 (sec). Leaf size: 24

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

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