29.3.20 problem 74

Internal problem ID [4682]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 3
Problem number : 74
Date solved : Monday, January 27, 2025 at 09:31:29 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }+\tan \left (x \right ) \left (1-y^{2}\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (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: 0.618 (sec). Leaf size: 45

DSolve[D[y[x],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*}