60.1.352 problem 353

Internal problem ID [10366]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 353
Date solved : Monday, January 27, 2025 at 07:33:05 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 12

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

\[ y = \arcsin \left (\frac {1}{c_{1} x}\right ) \]

✓ Solution by Mathematica

Time used: 11.816 (sec). Leaf size: 19

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

\begin{align*} y(x)\to \arcsin \left (\frac {e^{c_1}}{x}\right ) \\ y(x)\to 0 \\ \end{align*}