66.1.1 problem Problem 1

Internal problem ID [13848]
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 1
Date solved : Tuesday, January 28, 2025 at 06:05:03 AM
CAS classification : [_separable]

\begin{align*} \tan \left (y\right )-\cot \left (x \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.543 (sec). Leaf size: 9

dsolve(tan(y(x))-cot(x)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \arcsin \left (\sec \left (x \right ) c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.102 (sec). Leaf size: 80

DSolve[Tan[y[x]]-Cot[x]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^x(\cos (K[1]+y(x))-\cos (K[1]-y(x)))dK[1]+\int _1^{y(x)}\left (\cos (x-K[2])+\cos (x+K[2])-\int _1^x(-\sin (K[1]-K[2])-\sin (K[1]+K[2]))dK[1]\right )dK[2]=c_1,y(x)\right ] \]