Internal problem ID [2480]
Book: Differential equations, Shepley L. Ross, 1964
Section: 2.4, page 55
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_exponential_symmetries]]
Solve \begin {gather*} \boxed {2 x \tan \relax (y)+\left (x -x^{2} \tan \relax (y)\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 34
dsolve((2*x*tan(y(x)))+(x-x^2*tan(y(x)))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = 2 \RootOf \left ({\mathrm e}^{\textit {\_Z}} \left (\int _{}^{2 \textit {\_Z}}-\frac {{\mathrm e}^{-\frac {\textit {\_a}}{2}}}{2 \tan \left (\textit {\_a} \right )}d \textit {\_a} \right )+c_{1} {\mathrm e}^{\textit {\_Z}}-x \right ) \]
✓ Solution by Mathematica
Time used: 0.414 (sec). Leaf size: 78
DSolve[(2*x*Tan[y[x]])+(x-x^2*Tan[y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x=\frac {1}{34} \left ((8-2 i) e^{2 i y(x)} \, _2F_1\left (1,1+\frac {i}{4};2+\frac {i}{4};e^{2 i y(x)}\right )-34 i \, _2F_1\left (\frac {i}{4},1;1+\frac {i}{4};e^{2 i y(x)}\right )\right )+c_1 e^{\frac {y(x)}{2}},y(x)\right ] \]