Internal problem ID [564]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.6. Page 100
Problem number: 29.
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 \csc \relax (y) y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 15
dsolve(exp(x)+(exp(x)*cot(y(x))+2*csc(y(x))*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: 0.318 (sec). Leaf size: 18
DSolve[Exp[x]+(Exp[x]*Cot[y[x]]+2*Csc[y[x]]*y[x])*y'[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [y(x)^2+e^x \sin (y(x))=c_1,y(x)\right ] \]