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    Differential Equations
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    Find the order and degrees, if defined, of each of the following differential equations:
    straight x space straight y space fraction numerator straight d squared straight y over denominator dx squared end fraction plus straight x open parentheses dy over dx close parentheses squared minus straight y dy over dx space equals space 0
    The given differential equation is
    xy fraction numerator straight d squared straight y over denominator dx squared end fraction plus straight x open parentheses dy over dx close parentheses squared minus straight y dy over dx equals 0
    The highest order derivative present in the given differential equation is fraction numerator straight d squared straight y over denominator dx squared end fraction. So its order is two. It is a polynomial  equation in fraction numerator straight d squared straight y over denominator dx squared end fraction space and space dy over dx and the highest power raised to fraction numerator straight d squared straight y over denominator dx squared end fraction is one, so its degree is one. 
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    Answer
    Find the order and degree of the differential equation straight x dy over dx plus fraction numerator 3 over denominator begin display style dy over dx end style end fraction equals straight y squared state also if this is linear or non-linear. 

    The given differential equation is
                    straight x dy over dx plus fraction numerator 3 over denominator begin display style dy over dx end style end fraction equals straight y squared
    or   straight x open parentheses dy over dx close parentheses squared plus 3 space equals space straight y squared dy over dx
    or    straight x open parentheses dy over dx close parentheses squared minus straight y squared dy over dx plus 3 space equals space 0
    It is of order 1, degree 2 and non-linear.

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    Answer
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    Write the order and degree of the differential equation
    open parentheses fraction numerator straight d squared straight y over denominator dx squared end fraction close parentheses squared plus open parentheses dy over dx close parentheses cubed plus 2 straight y space equals space 0

    The given differential equation is
    open parentheses fraction numerator straight d squared straight y over denominator dx squared end fraction close parentheses squared plus open parentheses dy over dx close parentheses cubed plus 2 straight y space equals space 0
    Its order is 2 and degree is 2.

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    Find the order and degrees, if defined, of each of the following differential equations:
    dy over dx minus cosx space equals 0
    The given differential equation is dy over dx minus cosx space equals space 0.
    The highest order derivative present in the differential equation is dy over dx so its order is one. It is a  polynomial equation in dy over dx and the highest power raised to dy over dx is one, so its degree is one. 
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    Answer
    Find the order and degrees, if defined, of each the following differential equations:
    straight y to the power of straight m plus straight y squared plus straight e to the power of straight y space equals space 0
    The given differential equation is
    straight y to the power of straight m plus straight y squared plus straight e to the power of straight y equals 0
    The highest order derivative present in the differential equation is y''', so its order is three. The given differential equation is not a polynomial equation in its derivative and so its degree is not defined.
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