3.20 problem 74

Internal problem ID [3338]

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]

\[ \boxed {y^{\prime }+\tan \left (x \right ) \left (1-y^{2}\right )=0} \]

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)
 

\[ y \left (x \right ) = -\tanh \left (-\ln \left (\cos \left (x \right )\right )+c_{1} \right ) \]

Solution by Mathematica

Time used: 0.656 (sec). Leaf size: 45

DSolve[y'[x]+Tan[x] (1-y[x]^2)==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1-e^{2 c_1} \sec ^2(x)}{1+e^{2 c_1} \sec ^2(x)} y(x)\to -1 y(x)\to 1 \end{align*}