Internal problem ID [3351]
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]
\[ \boxed {y^{\prime }+\tan \left (x \right ) \sec \left (x \right ) y^{3}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 48
dsolve(diff(y(x),x)+y(x)^3*sec(x)*tan(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {\sqrt {\left (\cos \left (x \right ) c_{1} +2\right ) \cos \left (x \right )}}{\cos \left (x \right ) c_{1} +2} y \left (x \right ) = -\frac {\sqrt {\left (\cos \left (x \right ) c_{1} +2\right ) \cos \left (x \right )}}{\cos \left (x \right ) c_{1} +2} \end{align*}
✓ Solution by Mathematica
Time used: 0.386 (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*}