78.8.50 problem 50

Internal problem ID [18248]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 50
Date solved : Tuesday, January 28, 2025 at 11:44:13 AM
CAS classification : [_linear]

\begin{align*} x^{\prime }+x \cot \left (y \right )&=\sec \left (y \right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

dsolve(diff(x(y),y) + x(y)*cot(y) = sec(y),x(y), singsol=all)
 

\[ x \left (y \right ) = \left (-\ln \left (\cos \left (y \right )\right )+c_{1} \right ) \csc \left (y \right ) \]

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 16

DSolve[D[x[y],y] + x[y]*Cot[y] == Sec[y],x[y],y,IncludeSingularSolutions -> True]
 

\[ x(y)\to \csc (y) (-\log (\cos (y))+c_1) \]