Internal problem ID [4433]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page
46
Problem number: 28.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-2 y+2 y t=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve([diff(y(t),t)=2*y(t)-2*t*y(t),y(0) = 3],y(t), singsol=all)
\[ y \relax (t ) = 3 \,{\mathrm e}^{-t \left (t -2\right )} \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 15
DSolve[{y'[t]==2*y[t]-2*t*y[t],{y[0]==3}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 3 e^{-((t-2) t)} \\ \end{align*}