Internal problem ID [461]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.1. Page 40
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {2 y+y^{\prime }=t \,{\mathrm e}^{-2 t}} \] With initial conditions \begin {align*} [y \left (1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve([2*y(t)+diff(y(t),t) = t/exp(2*t),y(1) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (t^{2}-1\right ) {\mathrm e}^{-2 t}}{2} \]
✓ Solution by Mathematica
Time used: 0.054 (sec). Leaf size: 19
DSolve[{2*y[t]+y'[t] == t/Exp[2*t],y[1]==0},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} e^{-2 t} \left (t^2-1\right ) \]