Internal problem ID [4067]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 29
Problem number: 828.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_separable]
\[ \boxed {{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2}=0} \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 61
dsolve(diff(y(x),x)^2+2*y(x)*diff(y(x),x)*cot(x)-y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = 0 y \left (x \right ) = \frac {c_{1} \left (1+\tan \left (x \right )^{2}\right ) \sqrt {\frac {\tan \left (x \right )^{2}}{1+\tan \left (x \right )^{2}}}}{\left (1+\sqrt {1+\tan \left (x \right )^{2}}\right ) \tan \left (x \right )} y \left (x \right ) = \frac {c_{1} {\mathrm e}^{\operatorname {arctanh}\left (\frac {1}{\sqrt {1+\tan \left (x \right )^{2}}}\right )} \sqrt {1+\tan \left (x \right )^{2}}}{\tan \left (x \right )} \end{align*}
✓ Solution by Mathematica
Time used: 0.158 (sec). Leaf size: 36
DSolve[(y'[x])^2+2 y[x] y'[x] Cot[x]-y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \csc ^2\left (\frac {x}{2}\right ) y(x)\to c_1 \sec ^2\left (\frac {x}{2}\right ) y(x)\to 0 \end{align*}