78.1.25 problem 2 (k)

Internal problem ID [18080]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 2 (k)
Date solved : Tuesday, January 28, 2025 at 11:25:41 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.066 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 37.548 (sec). Leaf size: 23

DSolve[x*D[y[x],x]==(1-2*x^2)*Tan[y[x]],y[x],x,IncludeSingularSolutions -> True]
 

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