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    Could someone tell me simply, what is an exact differential equation.
    For this example, how do i determine whether it is an exact differential equation or not.

    Does it have to be in this form to be exact.
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    Is this the same as the differential equation above that you posted ?
     \displaystyle \frac{d}{dx} \left [x^3y \right ] = x
    The LHS is exactly the derivative of  x^3y .
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    (Original post by Fenugreek)
    Does it have to be in this form to be exact.
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    Yes, an exact differential equation is where one side can be re-written as \displaystyle \frac{\mathrm{d}}{\mathrm{d}x } \left( yf(x) \right)

    In this case, your DE is exact, because \displaystyle x^3 \frac{\mathrm{d}y}{\mathrm{d}x} + 3x^2 y = \frac{\mathrm{d}}{\mathrm{d}x } \left( x^3y\right).

    You can check this equality is true by differentiating x^3y with respect to x using the product rule.
 
 
 
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