Internal problem ID [15555]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 3. Section 24.2. Solving the Cauchy problem for linear differential equation with
constant coefficients. Exercises page 249
Problem number: 832.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {x^{\prime }-x=\cos \left (t \right )-\sin \left (t \right )} \] With initial conditions \begin {align*} [x \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.375 (sec). Leaf size: 6
dsolve([diff(x(t),t)-x(t)=cos(t)-sin(t),x(0) = 0],x(t), singsol=all)
\[ x \left (t \right ) = \sin \left (t \right ) \]
✓ Solution by Mathematica
Time used: 0.045 (sec). Leaf size: 7
DSolve[{x'[t]-x[t]==Cos[t]-Sin[t],{x[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \sin (t) \]