Internal problem ID [5475]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.8. Integrating Factors. Page
32
Problem number: 1(d).
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 {{\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \relax (y)+2 y \csc \relax (y)\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.059 (sec). Leaf size: 15
dsolve(exp(x)+(exp(x)*cot(y(x))+2*y(x)*csc(y(x)))*diff(y(x),x)=0,y(x), singsol=all)
\[ {\mathrm e}^{x} \sin \left (y \relax (x )\right )+y \relax (x )^{2}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.321 (sec). Leaf size: 18
DSolve[Exp[x]+(Exp[x]*Cot[y[x]]+2*y[x]*Csc[y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [y(x)^2+e^x \sin (y(x))=c_1,y(x)\right ] \]