Internal problem ID [10799]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {x^{\prime }-x \cot \left (t \right )-4 \sin \left (t \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.05 (sec). Leaf size: 14
DSolve[x'[t]-x[t]*Cot[t]==4*Sin[t],x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to (4 t+c_1) \sin (t) \\ \end{align*}