Internal problem ID [7934]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 354.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x)*G(y),0]]]
Solve \begin {gather*} \boxed {\left (x \sin \relax (y)-1\right ) y^{\prime }+\cos \relax (y)=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 115
dsolve((x*sin(y(x))-1)*diff(y(x),x)+cos(y(x)) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \arctan \left (-\frac {\left (c_{1} x +\sqrt {c_{1}^{2}-x^{2}+1}\right ) c_{1}}{c_{1}^{2}+1}+x , \frac {c_{1} x +\sqrt {c_{1}^{2}-x^{2}+1}}{c_{1}^{2}+1}\right ) \\ y \relax (x ) = \arctan \left (\frac {\left (-c_{1} x +\sqrt {c_{1}^{2}-x^{2}+1}\right ) c_{1}}{c_{1}^{2}+1}+x , -\frac {-c_{1} x +\sqrt {c_{1}^{2}-x^{2}+1}}{c_{1}^{2}+1}\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.296 (sec). Leaf size: 163
DSolve[Cos[y[x]] + (-1 + x*Sin[y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\text {ArcCos}\left (\frac {c_1 x-\sqrt {-x^2+1+c_1{}^2}}{1+c_1{}^2}\right ) \\ y(x)\to \text {ArcCos}\left (\frac {c_1 x-\sqrt {-x^2+1+c_1{}^2}}{1+c_1{}^2}\right ) \\ y(x)\to -\text {ArcCos}\left (\frac {\sqrt {-x^2+1+c_1{}^2}+c_1 x}{1+c_1{}^2}\right ) \\ y(x)\to \text {ArcCos}\left (\frac {\sqrt {-x^2+1+c_1{}^2}+c_1 x}{1+c_1{}^2}\right ) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}