76.4.23 problem 29

Internal problem ID [17417]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.6 (Exact equations and integrating factors). Problems at page 100
Problem number : 29
Date solved : Tuesday, January 28, 2025 at 10:06:30 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: 0.137 (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: 0.309 (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]
 

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