Internal problem ID [11519]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 3, Laplace transform. Section 3.2.1 Initial value problems. Exercises page
156
Problem number: 6(b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {x^{\prime }+x=\sin \left (2 t \right )} \] With initial conditions \begin {align*} [x \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve([diff(x(t),t)+x(t)=sin(2*t),x(0) = 0],x(t), singsol=all)
\[ x \left (t \right ) = -\frac {2 \cos \left (2 t \right )}{5}+\frac {\sin \left (2 t \right )}{5}+\frac {2 \,{\mathrm e}^{-t}}{5} \]
✓ Solution by Mathematica
Time used: 0.15 (sec). Leaf size: 27
DSolve[{x'[t]+x[t]==Sin[2*t],{x[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {1}{5} \left (2 e^{-t}+\sin (2 t)-2 \cos (2 t)\right ) \]