14.4.34 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 : Tuesday, September 30, 2025 at 06:54:41 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*}

✓ Maple. Time used: 0.076 (sec). Leaf size: 23

ode:=(1-3^(1/2))*diff(y(x),x)+y(x)*sec(x) = y(x)^(3^(1/2))*sec(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (-c_1 \tan \left (x \right )+1+c_1 \sec \left (x \right )\right )^{-\frac {1}{2}-\frac {\sqrt {3}}{2}} \]

✓ Mathematica. Time used: 0.418 (sec). Leaf size: 76

ode=(1-Sqrt[3])*D[y[x],x]+y[x]*Sec[x]==y[x]^Sqrt[3]*Sec[x]; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 51.289 (sec). Leaf size: 136

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)/cos(x) - y(x)**(sqrt(3))/cos(x) + (1 - sqrt(3))*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \left (\frac {i e^{\sqrt {3} C_{1}} + e^{\sqrt {3} C_{1} + i x}}{- i e^{C_{1}} + i e^{\sqrt {3} C_{1}} + e^{C_{1} + i x} + e^{\sqrt {3} C_{1} + i x}}\right )^{- \frac {1}{1 - \sqrt {3}}}, \ y{\left (x \right )} = \left (\frac {i e^{\sqrt {3} C_{1}} + e^{\sqrt {3} C_{1} + i x}}{i e^{C_{1}} + i e^{\sqrt {3} C_{1}} - e^{C_{1} + i x} + e^{\sqrt {3} C_{1} + i x}}\right )^{- \frac {1}{1 - \sqrt {3}}}\right ] \]