1.13 problem 3(b)

Internal problem ID [3041]

Book: Elementary Differential equations, Chaundy, 1969
Section: Exercises 3, page 60
Problem number: 3(b).
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

\[ \boxed {\cot \left (x \right ) y^{\prime }+y=\tan \left (x \right )} \]

✓ Solution by Maple

Time used: 0.0 (sec). Leaf size: 23

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

\[ y \left (x \right ) = \frac {\tan \left (x \right )}{2}-\frac {\cos \left (x \right ) \ln \left (\sec \left (x \right )+\tan \left (x \right )\right )}{2}+\cos \left (x \right ) c_{1} \]

✓ Solution by Mathematica

Time used: 0.071 (sec). Leaf size: 25

DSolve[Cot[x]*y'[x]+y[x]==Tan[x],y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

\[ y(x)\to \frac {1}{2} (\cos (x) (-\text {arctanh}(\sin (x)))+\tan (x)+2 c_1 \cos (x)) \]