Internal problem ID [11661]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number: 24.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {-x+x^{\prime }=\sin \left (2 t \right )} \] With initial conditions \begin {align*} [x \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
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: 0.083 (sec). Leaf size: 27
DSolve[{x'[t]-x[t]==Sin[2*t],{x[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {1}{5} \left (2 e^t-\sin (2 t)-2 \cos (2 t)\right ) \]