60.1.356 problem 357

Internal problem ID [10370]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 357
Date solved : Tuesday, January 28, 2025 at 04:37:51 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} x y^{\prime } \ln \left (x \right ) \sin \left (y\right )+\cos \left (y\right ) \left (1-x \cos \left (y\right )\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.062 (sec). Leaf size: 13

dsolve(x*diff(y(x),x)*ln(x)*sin(y(x))+cos(y(x))*(1-x*cos(y(x))) = 0,y(x), singsol=all)
 

\[ y = \operatorname {arcsec}\left (\frac {x +c_{1}}{\ln \left (x \right )}\right ) \]

✓ Solution by Mathematica

Time used: 1.075 (sec). Leaf size: 53

DSolve[Cos[y[x]]*(1 - x*Cos[y[x]]) + x*Log[x]*Sin[y[x]]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sec ^{-1}\left (\frac {x-c_1}{\log (x)}\right ) \\ y(x)\to \sec ^{-1}\left (\frac {x-c_1}{\log (x)}\right ) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}