Internal problem ID [2046]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 12, page 46
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
\[ \boxed {y^{\prime }+y \ln \left (y\right ) \tan \left (x \right )-2 y=0} \]
✓ Solution by Maple
Time used: 1.25 (sec). Leaf size: 25
dsolve(diff(y(x),x)+y(x)*ln(y(x))*tan(x)=2*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (-\frac {\cos \left (x \right )}{\sin \left (x \right )-1}\right )^{2 \cos \left (x \right )} {\mathrm e}^{\cos \left (x \right ) c_{1}} \]
✓ Solution by Mathematica
Time used: 2.002 (sec). Leaf size: 17
DSolve[y'[x]+y[x]*Log[y[x]]*Tan[x]==2*y[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{2 \cos (x) \left (\coth ^{-1}(\sin (x))+c_1\right )} \]