1.63 problem 64

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*}