1.13 problem 3(b)

Internal problem ID [2532]

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]

\[ \boxed {\cot \left (x \right ) y^{\prime }+y-\tan \left (x \right )=0} \]

Solution by Maple

Time used: 0.0 (sec). Leaf size: 31

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

\[ y \left (x \right ) = \left (\frac {\sin \left (x \right )^{3}}{2 \cos \left (x \right )^{2}}+\frac {\sin \left (x \right )}{2}-\frac {\ln \left (\sec \left (x \right )+\tan \left (x \right )\right )}{2}+c_{1} \right ) \cos \left (x \right ) \]

Solution by Mathematica

Time used: 0.064 (sec). Leaf size: 25

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

\begin{align*} y(x)\to \frac {1}{2} (\cos (x) (-\text {arctanh}(\sin (x)))+\tan (x)+2 c_1 \cos (x)) \\ \end{align*}