Internal problem ID [2989]
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]]
\[ \boxed {2 x \tan \left (y\right )+\left (x -x^{2} \tan \left (y\right )\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.093 (sec). Leaf size: 32
dsolve((2*x*tan(y(x)))+(x-x^2*tan(y(x)))*diff(y(x),x)=0,y(x), singsol=all)
\[ \frac {{\mathrm e}^{\frac {y \left (x \right )}{2}} \left (\int _{}^{y \left (x \right )}\cot \left (\textit {\_a} \right ) {\mathrm e}^{-\frac {\textit {\_a}}{2}}d \textit {\_a} \right )}{2}-{\mathrm e}^{\frac {y \left (x \right )}{2}} c_{1} +x = 0 \]
✓ Solution by Mathematica
Time used: 0.442 (sec). Leaf size: 78
DSolve[(2*x*Tan[y[x]])+(x-x^2*Tan[y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x=\frac {1}{34} \left ((8-2 i) e^{2 i y(x)} \operatorname {Hypergeometric2F1}\left (1,1+\frac {i}{4},2+\frac {i}{4},e^{2 i y(x)}\right )-34 i \operatorname {Hypergeometric2F1}\left (\frac {i}{4},1,1+\frac {i}{4},e^{2 i y(x)}\right )\right )+c_1 e^{\frac {y(x)}{2}},y(x)\right ] \]