13.2.10 problem 11

Internal problem ID [2308]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.2. Page 9
Problem number : 11
Date solved : Monday, January 27, 2025 at 05:45:14 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: 0.008 (sec). Leaf size: 12

dsolve([-2*t*y(t)+diff(y(t),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: 0.026 (sec). Leaf size: 18

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

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