Internal problem ID [1647]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.2. Page 6
Problem number: Example 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }+2 y t -t=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve([diff(y(t),t)+2*t*y(t)=t,y(1) = 2],y(t), singsol=all)
\[ y \relax (t ) = \frac {1}{2}+\frac {3 \,{\mathrm e}^{-\left (t -1\right ) \left (t +1\right )}}{2} \]
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 22
DSolve[{y'[t]+2*t*y[t]==t,y[1]==2},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {3 e^{1-t^2}}{2}+\frac {1}{2} \\ \end{align*}