Internal problem ID [10136]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 14. Equations
reducible to linear equations (Bernoulli). Page 21
Problem number: Ex 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } \sin \relax (y)+\sin \relax (x ) \cos \relax (y)-\sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 14
dsolve(sin(y(x))*diff(y(x),x)+sin(x)*cos(y(x))=sin(x),y(x), singsol=all)
\[ y \relax (x ) = \arccos \left ({\mathrm e}^{-\cos \relax (x )} c_{1}+1\right ) \]
✓ Solution by Mathematica
Time used: 8.68 (sec). Leaf size: 31
DSolve[Sin[y[x]]*y'[x]+Sin[x]*Cos[y[x]]==Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 0 \\ y(x)\to 2 \text {ArcSin}\left (e^{\frac {1}{4} (-2 \cos (x)+c_1)}\right ) \\ y(x)\to 0 \\ \end{align*}