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...Example exact differential equations professorrichardbrown problem solve the initial value x y xydy dx strategy solving this ode with an point means nding particular solution to that passes through in ty plane here we show is and use standard calculus integration dierentiation nd a function of both whose level sets are implicit general solutions then data indeed identify m as collection all terms not attached factor n xy coecient exactness condition thus know by theorem there exists where c can recover integrating partial derivatives st integrate get some specic information on z mdx h have good idea what looks like up unknown notice though constant may be because you antiderivative derivative respect antiderivatives will vary variable any alone would serve under need account for hence term consisting at end tocontinue now other work out rest calculate only so total last expression also professor richard brown conclude or realizing two constants really one since priori xyy ivp set our l...