Internal problem ID [2019]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 11, page 45
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [`y=_G(x,y')`]
\[ \boxed {\csc \left (y\right ) \cot \left (y\right ) y^{\prime }-\csc \left (y\right )={\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 16
dsolve(csc(y(x))*cot(y(x))*diff(y(x),x)=(csc(y(x))+exp(x)),y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {arccsc}\left (-\frac {{\mathrm e}^{x}}{2}+{\mathrm e}^{-x} c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 1.115 (sec). Leaf size: 30
DSolve[Csc[y[x]]*Cot[y[x]]*y'[x]==(Csc[y[x]]+Exp[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\csc ^{-1}\left (\frac {e^x}{2}-c_1 e^{-x}\right ) \\ y(x)\to 0 \\ \end{align*}