Internal problem ID [2841]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 4
Problem number: 90.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }+\left (\tan \relax (x )+y^{2} \sec \relax (x )\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 30
dsolve(diff(y(x),x)+(tan(x)+y(x)^2*sec(x))*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\cos \relax (x )}{\sqrt {2 \sin \relax (x )+c_{1}}} \\ y \relax (x ) = -\frac {\cos \relax (x )}{\sqrt {2 \sin \relax (x )+c_{1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.451 (sec). Leaf size: 48
DSolve[y'[x]+(Tan[x]+y[x]^2 Sec[x])y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{\sqrt {\sec ^2(x) (2 \sin (x)+c_1)}} \\ y(x)\to \frac {1}{\sqrt {\sec ^2(x) (2 \sin (x)+c_1)}} \\ y(x)\to 0 \\ \end{align*}