Internal problem ID [10976]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 5.6 Laplace transform. Nonhomogeneous equations. Problems page 368
Problem number: Problem 3(b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }-2 y-4 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -2\right )\right )=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 48
dsolve([diff(y(t),t)-2*y(t)=4*t*(Heaviside(t)-Heaviside(t-2)),y(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = 2 t \operatorname {Heaviside}\left (t -2\right )-2 t \operatorname {Heaviside}\left (t \right )+\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (t \right )-5 \operatorname {Heaviside}\left (t -2\right ) {\mathrm e}^{-4+2 t}+\operatorname {Heaviside}\left (t \right ) {\mathrm e}^{2 t}+{\mathrm e}^{2 t} \]
✓ Solution by Mathematica
Time used: 0.083 (sec). Leaf size: 47
DSolve[{y'[t]-2*y[t]==4*t*(UnitStep[t]-UnitStep[t-2]),{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to {cc} \{ & {cc} e^{2 t} & t<0 \\ e^{2 t-4} \left (-5+2 e^4\right ) & t>2 \\ -2 t+2 e^{2 t}-1 & \text {True} \\ \\ \\ \\ \\ \end{align*}