44.2.6 problem 1(f)

Internal problem ID [9098]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.3 SEPARABLE EQUATIONS. Page 12
Problem number : 1(f)
Date solved : Tuesday, September 30, 2025 at 06:04:10 PM
CAS classification : [_separable]

\begin{align*} x y^{\prime }&=\left (-4 x^{2}+1\right ) \tan \left (y\right ) \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 16

ode:=x*diff(y(x),x) = (-4*x^2+1)*tan(y(x)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \arcsin \left (\frac {x \,{\mathrm e}^{-2 x^{2}}}{c_1}\right ) \]

✓ Mathematica. Time used: 37.731 (sec). Leaf size: 23

ode=x*D[y[x],x]==(1-4*x^2)*Tan[y[x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \arcsin \left (x e^{-2 x^2+c_1}\right )\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.303 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) - (1 - 4*x**2)*tan(y(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \pi - \operatorname {asin}{\left (C_{1} x e^{- 2 x^{2}} \right )}, \ y{\left (x \right )} = \operatorname {asin}{\left (C_{1} x e^{- 2 x^{2}} \right )}\right ] \]