50.2.6 problem 1(f)

Internal problem ID [7812]
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 : Monday, January 27, 2025 at 03:23:49 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 16

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

\[ y = \arcsin \left (\frac {x \,{\mathrm e}^{-2 x^{2}}}{c_{1}}\right ) \]

✓ Solution by Mathematica

Time used: 39.484 (sec). Leaf size: 23

DSolve[x*D[y[x],x]==(1-4*x^2)*Tan[y[x]],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*}