75.6.37 problem 170

Internal problem ID [16793]
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
Date solved : Tuesday, January 28, 2025 at 08:26:22 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y^{\prime }+x \sin \left (2 y\right )&=2 x \,{\mathrm e}^{-x^{2}} \cos \left (y\right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.012 (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)
 

\[ y = \arctan \left (\left (x^{2}+2 c_{1} \right ) {\mathrm e}^{-x^{2}}\right ) \]

✓ Solution by Mathematica

Time used: 9.898 (sec). Leaf size: 70

DSolve[D[y[x],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*}