69.33.5 problem 834

Internal problem ID [18574]
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 : Thursday, October 02, 2025 at 03:15:02 PM
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*}

✓ Maple. Time used: 0.096 (sec). Leaf size: 15

ode:=diff(x(t),t)+x(t) = 2*sin(t); 
ic:=[x(0) = 0]; 
dsolve([ode,op(ic)],x(t),method='laplace');
 

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

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 27

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

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

✓ Sympy. Time used: 0.074 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(x(t) - 2*sin(t) + Derivative(x(t), t),0) 
ics = {x(0): 0} 
dsolve(ode,func=x(t),ics=ics)
 

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