28.1.63 problem 64

Internal problem ID [4369]
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
Date solved : Monday, January 27, 2025 at 09:09:23 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=1+3 y \tan \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (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: 0.047 (sec). Leaf size: 26

DSolve[D[y[x],x]==1+3*y[x]*Tan[x],y[x],x,IncludeSingularSolutions -> True]
 

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