1.12 problem 3(a)

Internal problem ID [2531]

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

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {\cot \relax (x ) y^{\prime }+y-x=0} \end {gather*}

Solution by Maple

Time used: 0.005 (sec). Leaf size: 23

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

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

Solution by Mathematica

Time used: 0.08 (sec). Leaf size: 45

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

\begin{align*} y(x)\to x+\cos (x) \left (\log \left (\cos \left (\frac {x}{2}\right )-\sin \left (\frac {x}{2}\right )\right )-\log \left (\sin \left (\frac {x}{2}\right )+\cos \left (\frac {x}{2}\right )\right )+c_1\right ) \\ \end{align*}