28.1.75 problem 78

Internal problem ID [4381]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 78
Date solved : Sunday, March 30, 2025 at 03:11:12 AM
CAS classification : [_Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 12

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

\[ y = \frac {\sec \left (x \right )}{x +c_1} \]

✓ Mathematica. Time used: 0.205 (sec). Leaf size: 19

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

\begin{align*} y(x)\to \frac {\sec (x)}{x+c_1} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.263 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = \frac {1}{\left (C_{1} + x\right ) \cos {\left (x \right )}} \]