1.63 problem 64

Internal problem ID [3208]

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]

\[ \boxed {y^{\prime }-3 y \tan \left (x \right )=1} \]

Solution by Maple

Time used: 0.016 (sec). Leaf size: 23

dsolve(diff(y(x),x)=1+3*y(x)*tan(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\tan \left (x \right )}{3}+\sec \left (x \right )^{3} c_{1} +\frac {2 \sec \left (x \right )^{2} \tan \left (x \right )}{3} \]

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]
 

\[ y(x)\to \frac {1}{12} \sec ^3(x) (9 \sin (x)+\sin (3 x)+12 c_1) \]