# Differential equations cannot spot any standard form

How to approach the Differential equation $$2(x-y \, \sin(2x)) \, dx + (3y^{2} + \cos(2x)) \, dy=0$$ I cannot see whether the equation is in any standard form. Initial steps and/or hints appreciated.

• Have you heard of "exact differential equation"? – bof Sep 17 '18 at 6:15
• The DE is in the form $M(x,y)dx+N(x,y)dy=0.$ What is the partial derivative of $M$ with rspect to $y$? What is the partial derivative of $N$ with respect to $x$? – bof Sep 17 '18 at 6:17
• Is x and y supposed to be some function of time or something? Your notation looks a lot like a differential form. – user2662833 Sep 17 '18 at 6:36
• Thank you. I had already done it. It was very easy infact. – Arka Seth Sep 17 '18 at 8:43
• @user2662833. Divide the equation formally with $dx$ and — voilà — a differential equation appears. – md2perpe Sep 17 '18 at 17:50

$$2(x-y \, \sin(2x)) \, dx + (3y^{2} + \cos(2x)) \, dy=0$$ $$2(x-y \, \sin(2x)) + (3y^{2} + \cos(2x)) y'=0$$ $$2x +(y\cos(2x))'+(y^3)'=0$$ Integrate $$x^2 +y\cos(2x)+y^3=K$$