83.5.1 problem 1

Internal problem ID [19096]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (D) at page 16
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 12:55:54 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\cot \left (x \right ) y&=2 \cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 16

dsolve(diff(y(x),x)+y(x)*cot(x)=2*cos(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \csc \left (x \right ) \left (-\cos \left (x \right )^{2}+c_{1} +\frac {1}{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 20

DSolve[D[y[x],x]+y[x]*Cot[x]==2*Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {1}{2} \csc (x) (\cos (2 x)-2 c_1) \]