Internal problem ID [5391]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x y^{\prime }-\left (-4 x^{2}+1\right ) \tan \relax (y)=0} \end {gather*}
✓ Solution by Maple
Time used: 0.018 (sec). Leaf size: 16
dsolve(x*diff(y(x),x)=(1-4*x^2)*tan(y(x)),y(x), singsol=all)
\[ y \relax (x ) = \arcsin \left (\frac {x \,{\mathrm e}^{-2 x^{2}}}{c_{1}}\right ) \]
✓ Solution by Mathematica
Time used: 24.393 (sec). Leaf size: 23
DSolve[x*y'[x]==(1-4*x^2)*Tan[y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {ArcSin}\left (x e^{-2 x^2+c_1}\right ) \\ y(x)\to 0 \\ \end{align*}