75.33.3 problem 832

Internal problem ID [17285]
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
Date solved : Tuesday, January 28, 2025 at 09:58:54 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} x^{\prime }-x&=\cos \left (t \right )-\sin \left (t \right ) \end{align*}

Using Laplace method With initial conditions

\begin{align*} x \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 8.782 (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: 0.041 (sec). Leaf size: 7

DSolve[{D[x[t],t]-x[t]==Cos[t]-Sin[t],{x[0]==0}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \sin (t) \]