Internal problem ID [3350]
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]
\[ \boxed {y^{\prime }+\left (\tan \left (x \right )+y^{2} \sec \left (x \right )\right ) y=0} \]
✓ Solution by Maple
Time used: 0.031 (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 \left (x \right ) &= \frac {\cos \left (x \right )}{\sqrt {2 \sin \left (x \right )+c_{1}}} \\ y \left (x \right ) &= -\frac {\cos \left (x \right )}{\sqrt {2 \sin \left (x \right )+c_{1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 3.746 (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*}