Internal problem ID [14942]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 1. Basic concepts and definitions. Exercises page 18
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }+\cot \left (y\right )=1} \]
✓ Solution by Maple
Time used: 0.14 (sec). Leaf size: 29
dsolve(diff(y(x),x)=1-cot(y(x)),y(x), singsol=all)
\[ x +\frac {\ln \left (\csc \left (y \left (x \right )\right )^{2}\right )}{4}+\frac {\pi }{4}-\frac {\ln \left (-1+\cot \left (y \left (x \right )\right )\right )}{2}-\frac {y \left (x \right )}{2}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.376 (sec). Leaf size: 69
DSolve[y'[x]==1-Cot[y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [\left (\frac {1}{4}+\frac {i}{4}\right ) \log (-\tan (\text {$\#$1})+i)-\frac {1}{2} \log (1-\tan (\text {$\#$1}))+\left (\frac {1}{4}-\frac {i}{4}\right ) \log (\tan (\text {$\#$1})+i)\&\right ][-x+c_1] \\ y(x)\to \frac {\pi }{4} \\ \end{align*}