66.1.9 problem Problem 9

Internal problem ID [13856]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 1, First-Order Differential Equations. Problems page 88
Problem number : Problem 9
Date solved : Tuesday, January 28, 2025 at 06:05:29 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 17

dsolve(diff(x(t),t)=x(t)+sin(t),x(t), singsol=all)
 

\[ x \left (t \right ) = -\frac {\cos \left (t \right )}{2}-\frac {\sin \left (t \right )}{2}+c_{1} {\mathrm e}^{t} \]

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 29

DSolve[D[x[t],t]==x[t]+Sin[t],x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to e^t \left (\int _1^te^{-K[1]} \sin (K[1])dK[1]+c_1\right ) \]