Internal problem ID [2699]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 64.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }-1-3 y \tan \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 30
dsolve(diff(y(x),x)=1+3*y(x)*tan(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {9 \sin \relax (x )+\sin \left (3 x \right )+12 c_{1}}{3 \cos \left (3 x \right )+9 \cos \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 26
DSolve[y'[x]==1+3*y[x]*Tan[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{12} \sec ^3(x) (9 \sin (x)+\sin (3 x)+12 c_1) \\ \end{align*}