78.5.4 problem 2 (d)

Internal problem ID [18147]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 9 (Integrating Factors). Problems at page 80
Problem number : 2 (d)
Date solved : Tuesday, January 28, 2025 at 11:34:03 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} {\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 y \csc \left (y\right )\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.015 (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)
 

\[ {\mathrm e}^{x} \sin \left (y\right )+y^{2}+c_1 = 0 \]

✓ Solution by Mathematica

Time used: 0.302 (sec). Leaf size: 18

DSolve[Exp[x]+(Exp[x]*Cot[y[x]]+2*y[x]*Csc[y[x]])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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