Internal problem ID [2189]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page
79
Problem number: Problem 50.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (1-\sqrt {3}\right ) y^{\prime }+y \sec \left (x \right )-y^{\sqrt {3}} \sec \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 54
dsolve((1-sqrt(3))*diff(y(x),x)+y(x)*sec(x)=y(x)^sqrt(3)*sec(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (\frac {c_{1} \cos \left (x \right )+\sin \left (x \right )+1}{\sin \left (x \right )+1}\right )^{-\frac {\sqrt {3}}{2}}}{\sqrt {\frac {\cos \left (x \right ) c_{1}}{\sin \left (x \right )+1}+\frac {\sin \left (x \right )}{\sin \left (x \right )+1}+\frac {1}{\sin \left (x \right )+1}}} \]
✓ Solution by Mathematica
Time used: 0.573 (sec). Leaf size: 74
DSolve[(1-Sqrt[3])*y'[x]+y[x]*Sec[x]==y[x]^Sqrt[3]*Sec[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [\frac {\log \left (1-\text {$\#$1}^{\sqrt {3}-1}\right )-\left (\sqrt {3}-1\right ) \log (\text {$\#$1})}{\sqrt {3}-1}\&\right ]\left [-\left (1+\sqrt {3}\right ) \text {arctanh}\left (\tan \left (\frac {x}{2}\right )\right )+c_1\right ] \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}