38.2.25 problem 25

Internal problem ID [6454]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Further problems 24. page 1068
Problem number : 25
Date solved : Wednesday, March 05, 2025 at 12:45:58 AM
CAS classification : [_Bernoulli]

\begin{align*} y^{\prime }+y \tan \left (x \right )&=y^{3} \sec \left (x \right )^{4} \end{align*}

✓ Maple. Time used: 0.018 (sec). Leaf size: 68

ode:=diff(y(x),x)+y(x)*tan(x) = y(x)^3*sec(x)^4; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {\sqrt {\cos \left (x \right )^{5} \left (\cos \left (x \right ) c_1 -2 \sin \left (x \right )\right )}\, \sec \left (x \right )}{\cos \left (x \right ) c_1 -2 \sin \left (x \right )} \\ y &= \frac {\sqrt {\cos \left (x \right )^{5} \left (\cos \left (x \right ) c_1 -2 \sin \left (x \right )\right )}\, \sec \left (x \right )}{\cos \left (x \right ) c_1 -2 \sin \left (x \right )} \\ \end{align*}

✓ Mathematica. Time used: 4.134 (sec). Leaf size: 48

ode=D[y[x],x]+y[x]*Tan[x]==y[x]^3*Sec[x]^4; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\frac {1}{\sqrt {\sec ^2(x) (-2 \tan (x)+c_1)}} \\ y(x)\to \frac {1}{\sqrt {\sec ^2(x) (-2 \tan (x)+c_1)}} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 1.231 (sec). Leaf size: 42

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x)**3/cos(x)**4 + y(x)*tan(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \sqrt {\frac {\cos ^{3}{\left (x \right )}}{C_{1} \cos {\left (x \right )} - 2 \sin {\left (x \right )}}}, \ y{\left (x \right )} = \sqrt {\frac {\cos ^{3}{\left (x \right )}}{C_{1} \cos {\left (x \right )} - 2 \sin {\left (x \right )}}}\right ] \]