66.1.36 problem Problem 50

Internal problem ID [13883]
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 50
Date solved : Tuesday, January 28, 2025 at 06:07:11 AM
CAS classification : [_linear]

\begin{align*} x^{\prime }-x \cot \left (t \right )&=4 \sin \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 12

dsolve(diff(x(t),t)-x(t)*cot(t)=4*sin(t),x(t), singsol=all)
 

\[ x \left (t \right ) = \left (4 t +c_{1} \right ) \sin \left (t \right ) \]

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 14

DSolve[D[x[t],t]-x[t]*Cot[t]==4*Sin[t],x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to (4 t+c_1) \sin (t) \]