83.43.2 problem Ex 3 page 7

Internal problem ID [19510]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter II. Equations of first order and first degree
Problem number : Ex 3 page 7
Date solved : Tuesday, January 28, 2025 at 01:47:10 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 3.004 (sec). Leaf size: 11

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

\[ y \left (x \right ) = \arccos \left (\frac {\csc \left (x \right )}{c_{1}}\right ) \]

✓ Solution by Mathematica

Time used: 5.513 (sec). Leaf size: 47

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

\begin{align*} y(x)\to -\arccos \left (-\frac {1}{2} c_1 \csc (x)\right ) \\ y(x)\to \arccos \left (-\frac {1}{2} c_1 \csc (x)\right ) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}