78.8.27 problem 27

Internal problem ID [18225]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 27
Date solved : Tuesday, January 28, 2025 at 11:40:49 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 26

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

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