21.1.2 problem 2

Internal problem ID [4078]
Book : Differential equations, Shepley L. Ross, 1964
Section : 2.4, page 55
Problem number : 2
Date solved : Monday, January 27, 2025 at 08:07:39 AM
CAS classification : [[_1st_order, _with_exponential_symmetries]]

\begin{align*} 2 x \tan \left (y\right )+\left (x -x^{2} \tan \left (y\right )\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.087 (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: 0.419 (sec). Leaf size: 78

DSolve[(2*x*Tan[y[x]])+(x-x^2*Tan[y[x]])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x=\frac {1}{34} \left ((8-2 i) e^{2 i y(x)} \operatorname {Hypergeometric2F1}\left (1,1+\frac {i}{4},2+\frac {i}{4},e^{2 i y(x)}\right )-34 i \operatorname {Hypergeometric2F1}\left (\frac {i}{4},1,1+\frac {i}{4},e^{2 i y(x)}\right )\right )+c_1 e^{\frac {y(x)}{2}},y(x)\right ] \]