Internal problem ID [924]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (\sec ^{2}\relax (y)\right ) y^{\prime }-3 \tan \relax (y)+1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(sec(y(x))^2*diff(y(x),x)-3*tan(y(x))= -1,y(x), singsol=all)
\[ y \relax (x ) = \arctan \left (\frac {c_{1} {\mathrm e}^{3 x}}{3}+\frac {1}{3}\right ) \]
✓ Solution by Mathematica
Time used: 22.719 (sec). Leaf size: 251
DSolve[Sec[y[x]]^2*y'[x]-3*Tan[y[x]]== -1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\text {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 \text {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 -\text {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 \text {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 -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ y(x)\to \text {ArcTan}(3)+\frac {\pi }{2} \\ y(x)\to \text {ArcTan}(3)-\frac {\pi }{2} \\ y(x)\to \text {ArcCos}\left (\frac {3}{\sqrt {10}}\right ) \\ y(x)\to -\text {ArcTan}(3)-\frac {\pi }{2} \\ y(x)\to \cot ^{-1}(3) \\ \end{align*}