6.4 problem 1(d)

Internal problem ID [6228]

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]`]]

\[ \boxed {\left ({\mathrm e}^{x} \cot \left (y\right )+2 y \csc \left (y\right )\right ) y^{\prime }=-{\mathrm e}^{x}} \]

Solution by Maple

Time used: 0.031 (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)
 

\[ {\mathrm e}^{x} \sin \left (y \left (x \right )\right )+y \left (x \right )^{2}+c_{1} = 0 \]

Solution by Mathematica

Time used: 0.322 (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]
 

\[ \text {Solve}\left [y(x)^2+e^x \sin (y(x))=c_1,y(x)\right ] \]