12.2.38 problem 48(a)

Internal problem ID [1574]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number : 48(a)
Date solved : Monday, January 27, 2025 at 05:00:50 AM
CAS classification : [_quadrature]

\begin{align*} \sec \left (y\right )^{2} y^{\prime }-3 \tan \left (y\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 14

dsolve(sec(y(x))^2*diff(y(x),x)-3*tan(y(x))= -1,y(x), singsol=all)
 

\[ y = \arctan \left (\frac {c_1 \,{\mathrm e}^{3 x}}{3}+\frac {1}{3}\right ) \]

✓ Solution by Mathematica

Time used: 60.185 (sec). Leaf size: 177

DSolve[Sec[y[x]]^2*D[y[x],x]-3*Tan[y[x]]== -1,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\arccos \left (-\frac {3 e^{6 c_1}}{\sqrt {e^{6 x}-2 e^{3 x+6 c_1}+10 e^{12 c_1}}}\right ) \\ y(x)\to \arccos \left (-\frac {3 e^{6 c_1}}{\sqrt {e^{6 x}-2 e^{3 x+6 c_1}+10 e^{12 c_1}}}\right ) \\ y(x)\to -\arccos \left (\frac {3 e^{6 c_1}}{\sqrt {e^{6 x}-2 e^{3 x+6 c_1}+10 e^{12 c_1}}}\right ) \\ y(x)\to \arccos \left (\frac {3 e^{6 c_1}}{\sqrt {e^{6 x}-2 e^{3 x+6 c_1}+10 e^{12 c_1}}}\right ) \\ \end{align*}