Determine order and degree (if defined) of differential equation
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    Differential Equations
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    Determine order and degree (if defined) of differential equations:
    open parentheses fraction numerator straight d squared straight y over denominator dx squared end fraction close parentheses squared plus cos open parentheses dy over dx close parentheses 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 cos open parentheses dy over dx close parentheses space equals space 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. therefore, its order is 2. Since the given differential equation is not a polynomial in dy over dx. therefore, its degree is not defined. 

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    Answer
    Determine order and degree (if defined) of differential equations:
    open parentheses ds over dt close parentheses to the power of 4 plus 3 straight s fraction numerator straight d squared straight s over denominator dt squared end fraction equals 0
    The given differential equation is
    open parentheses ds over dt close parentheses to the power of 4 plus 3 straight s fraction numerator straight d squared straight s over denominator dt squared end fraction equals space 0
    The highest order derivative present in the differential equation is fraction numerator straight d squared straight s over denominator dt squared end fraction
    ∴  its order is 2
    The highest power raised to fraction numerator straight d squared straight s over denominator dt squared end fraction is one, so its degree is 1.
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    Answer
    Determine order and degree (if defined) of differential equations:
    straight y apostrophe plus 5 space straight y equals 0
    The given differential equation is
    y' + 5 y = 0
    The highest order derivative present in the given differential equation is y' and index of its highest power is one.
    ∴    the given differential equation is of order 1 and degree 1.
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    Answer
    Determine order and degree (if defined) of differential equations:
    fraction numerator straight d squared straight y over denominator dx squared end fraction equals cos space 3 straight x plus space sin space 3 straight x
    The given differential equation is
    fraction numerator straight d squared straight y over denominator dx squared end fraction space equals space cos 3 straight x space plus space sin 3 straight x
    The highest order derivative present in the given differential equation is fraction numerator straight d squared straight y over denominator dx squared end fraction and index of its highest power is 1.
    ∴   the given differential equation is of order is 2 and degree 1.
    136 Views
    Answer
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    Determine order and degree (if defined) of differential equations:
    fraction numerator straight d to the power of 4 straight y over denominator dx to the power of 4 end fraction plus sin left parenthesis straight y to the power of straight m right parenthesis space equals space 0

    The given differential equation is
    fraction numerator straight d to the power of 4 straight y over denominator dx to the power of 4 end fraction plus sin left parenthesis straight y to the power of straight m right parenthesis space equals space 0
    The highest order derivative present in the differential equation is fraction numerator straight d to the power of 4 straight y over denominator dx to the power of 4 end fraction
    ∴  its order is 4
    The given differential equation is not a polynomial equation in its derivative and so its degree is not defined.
    354 Views
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