29.4.3 problem 90

Internal problem ID [4694]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 4
Problem number : 90
Date solved : Tuesday, March 04, 2025 at 07:04:28 PM
CAS classification : [_Bernoulli]

\begin{align*} y^{\prime }+\left (\tan \left (x \right )+y^{2} \sec \left (x \right )\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.027 (sec). Leaf size: 30

ode:=diff(y(x),x)+(tan(x)+y(x)^2*sec(x))*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y \left (x \right ) &= \frac {\cos \left (x \right )}{\sqrt {2 \sin \left (x \right )+c_{1}}} \\ y \left (x \right ) &= -\frac {\cos \left (x \right )}{\sqrt {2 \sin \left (x \right )+c_{1}}} \\ \end{align*}

✓ Mathematica. Time used: 3.81 (sec). Leaf size: 48

ode=D[y[x],x]+(Tan[x]+y[x]^2 Sec[x])y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.985 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((y(x)**2/cos(x) + tan(x))*y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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