Internal problem ID [2842]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 4
Problem number: 91.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }+y^{3} \sec \relax (x ) \tan \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 48
dsolve(diff(y(x),x)+y(x)^3*sec(x)*tan(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {\left (\cos \relax (x ) c_{1}+2\right ) \cos \relax (x )}}{\cos \relax (x ) c_{1}+2} \\ y \relax (x ) = -\frac {\sqrt {\left (\cos \relax (x ) c_{1}+2\right ) \cos \relax (x )}}{\cos \relax (x ) c_{1}+2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.319 (sec). Leaf size: 49
DSolve[y'[x]+y[x]^3 Sec[x] Tan[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{\sqrt {2} \sqrt {\sec (x)-c_1}} \\ y(x)\to \frac {1}{\sqrt {2} \sqrt {\sec (x)-c_1}} \\ y(x)\to 0 \\ \end{align*}