Internal problem ID [2842]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth
edition, 2015
Section: Chapter 10, The Laplace Transform and Some Elementary Applications. Exercises for
10.4. page 689
Problem number: Problem 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+2 y=4 t} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 1.703 (sec). Leaf size: 15
dsolve([diff(y(t),t)+2*y(t)=4*t,y(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = 2 t +2 \,{\mathrm e}^{-2 t}-1 \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 17
DSolve[{y'[t]+2*y[t]==4*t,{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to 2 t+2 e^{-2 t}-1 \]