Internal problem ID [3157]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 15
Problem number: 411.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (1-4 \left (\cos ^{2}\relax (x )\right )\right ) y^{\prime }-\tan \relax (x ) \left (1+4 \left (\cos ^{2}\relax (x )\right )\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve((1-4*cos(x)^2)*diff(y(x),x) = tan(x)*(1+4*cos(x)^2)*y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (1+2 \cos \left (2 x \right )\right )}{\cos \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.15 (sec). Leaf size: 23
DSolve[(1-4 Cos[x]^2)y'[x]==Tan[x](1+4 Cos[x]^2)y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 (2 \cos (2 x)+1) \sec (x) \\ y(x)\to 0 \\ \end{align*}