Internal problem ID [2829]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 3
Problem number: 74.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }+\tan \relax (x ) \left (1-y^{2}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve(diff(y(x),x)+tan(x)*(1-y(x)^2) = 0,y(x), singsol=all)
\[ y \relax (x ) = -\tanh \left (-\ln \left (\cos \relax (x )\right )+c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.702 (sec). Leaf size: 34
DSolve[y'[x]+Tan[x] (1-y[x]^2)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -1+\frac {2}{1+e^{2 c_1} \sec ^2(x)} \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}