75.33.5 problem 834

Internal problem ID [17287]
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 : 834
Date solved : Tuesday, January 28, 2025 at 09:58:55 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} x^{\prime }+x&=2 \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: 9.448 (sec). Leaf size: 15

dsolve([diff(x(t),t)+x(t)=2*sin(t),x(0) = 0],x(t), singsol=all)
 

\[ x \left (t \right ) = -\cos \left (t \right )+\sin \left (t \right )+{\mathrm e}^{-t} \]

✓ Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 27

DSolve[{D[x[t],t]+x[t]==2*Sin[t],{x[0]==0}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to e^{-t} \int _0^t2 e^{K[1]} \sin (K[1])dK[1] \]