Internal problem ID [15063]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page
54
Problem number: 170.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [`y=_G(x,y')`]
\[ \boxed {y^{\prime }+x \sin \left (2 y\right )-2 x \,{\mathrm e}^{-x^{2}} \cos \left (y\right )^{2}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve(diff(y(x),x)+x*sin(2*y(x))=2*x*exp(-x^2)*cos(y(x))^2,y(x), singsol=all)
\[ y \left (x \right ) = \arctan \left (\left (x^{2}+2 c_{1} \right ) {\mathrm e}^{-x^{2}}\right ) \]
✓ Solution by Mathematica
Time used: 10.038 (sec). Leaf size: 70
DSolve[y'[x]+x*Sin[2*y[x]]==2*x*Exp[-x^2]*Cos[y[x]]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \arctan \left (e^{-x^2} \left (x^2+c_1\right )\right ) \\ y(x)\to -\frac {1}{2} \pi e^{x^2} \sqrt {e^{-2 x^2}} \\ y(x)\to \frac {1}{2} \pi e^{x^2} \sqrt {e^{-2 x^2}} \\ \end{align*}