15.8.14 problem 14

Internal problem ID [3017]
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
Date solved : Monday, January 27, 2025 at 07:08:47 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} y^{\prime }+y \ln \left (y\right ) \tan \left (x \right )&=2 y \end{align*}

✓ Solution by Maple

Time used: 3.050 (sec). Leaf size: 25

dsolve(diff(y(x),x)+y(x)*ln(y(x))*tan(x)=2*y(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 2.029 (sec). Leaf size: 17

DSolve[D[y[x],x]+y[x]*Log[y[x]]*Tan[x]==2*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 \cos (x) \left (\coth ^{-1}(\sin (x))+c_1\right )} \]