15.7.9 problem 9

Internal problem ID [2990]
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
Date solved : Monday, January 27, 2025 at 07:05:56 AM
CAS classification : [`y=_G(x,y')`]

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

✓ 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)
 

\[ y = \operatorname {arccsc}\left (-\frac {{\mathrm e}^{x}}{2}+{\mathrm e}^{-x} c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 1.162 (sec). Leaf size: 30

DSolve[Csc[y[x]]*Cot[y[x]]*D[y[x],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*}