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