20.4.34 problem Problem 50

Internal problem ID [3669]
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
Date solved : Monday, January 27, 2025 at 07:53:43 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.252 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 0.570 (sec). Leaf size: 76

DSolve[(1-Sqrt[3])*D[y[x],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 [-\frac {2 \text {arctanh}\left (\tan \left (\frac {x}{2}\right )\right )}{\sqrt {3}-1}+c_1\right ] \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}