75.1.9 problem 10

Internal problem ID [16672]
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
Date solved : Tuesday, January 28, 2025 at 09:17:37 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=1-\cot \left (y\right ) \end{align*}

✓ Solution by Maple

Time used: 0.317 (sec). Leaf size: 29

dsolve(diff(y(x),x)=1-cot(y(x)),y(x), singsol=all)
 

\[ x +\frac {\ln \left (\csc \left (y\right )^{2}\right )}{4}+\frac {\pi }{4}-\frac {\ln \left (-1+\cot \left (y\right )\right )}{2}-\frac {y}{2}+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.365 (sec). Leaf size: 69

DSolve[D[y[x],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*}