Internal problem ID [1966]
Book: Ordinary Differential Equations, Robert H. Martin, 1983
Section: Problem 1.2-1, page 12
Problem number: 1.2-1 (i).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }-\tan \relax (t ) y-\left (\sec ^{3}\relax (t )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 13
dsolve(diff(y(t),t)=y(t)*tan(t)+sec(t)^3,y(t), singsol=all)
\[ y \relax (t ) = \frac {\tan \relax (t )+c_{1}}{\cos \relax (t )} \]
✓ Solution by Mathematica
Time used: 0.063 (sec). Leaf size: 13
DSolve[y'[t]==y[t]*Tan[t]+Sec[t]^3,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \sec (t) (\tan (t)+c_1) \\ \end{align*}