Important Questions of Differential Equations Mathematics | Zigya
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    Mathematics : Differential Equations

    Multiple Choice QuestionsShort Answer Type

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    21.

    Determine the order and degree of the differential equation:
    square root of straight x fraction numerator straight d to the power of 4 straight y over denominator dx to the power of 4 end fraction plus 5 open parentheses dy over dx close parentheses squared space equals 2 straight y squared minus straight x

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    Multiple Choice QuestionsMultiple Choice Questions

    22. The degree of the differential equation open parentheses fraction numerator straight d squared straight y over denominator dx squared end fraction close parentheses cubed plus open parentheses dy over dx close parentheses squared plus sin open parentheses dy over dx close parentheses plus 1 space space equals space 0 is

    • 3

    • 2

    • 1

    • 1

    95 Views
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    23. The degree of the differential equation 2 straight x squared fraction numerator straight d squared straight y over denominator dx squared end fraction minus 3 dy over dx plus straight y space equals space 0  is

    • 2

    • 1

    • 0

    • 0

    99 Views
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    Multiple Choice QuestionsShort Answer Type

    24. Verify that y = A cor x – B sin x is a solution of the differential equation
    fraction numerator straight d squared straight y over denominator dx squared end fraction plus straight y space equals space 0.
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    25. Verify that the function y = a cos x + b sin x, where a, b ∊ R is a solution of the differential equation fraction numerator straight d squared straight y over denominator dx squared end fraction plus straight y space equals space 0.
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    Multiple Choice QuestionsLong Answer Type

    26. Verify that y - 3 cos (log x) + 4 sin (log x) is a solution of the differential equation straight x squared fraction numerator straight d squared straight y over denominator dx squared end fraction plus straight x dy over dx plus straight y space equals space 0.
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    Multiple Choice QuestionsShort Answer Type

    27. Verify that the function y = e–3x is a solution of the differential equation fraction numerator straight d squared straight y over denominator dx squared end fraction plus dy over dx minus 6 straight y space equals space 0
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    28. Show that the function y = ae2X + be–x is a solution of differential equation fraction numerator straight d squared straight y over denominator dx squared end fraction minus dy over dx minus 2 straight y space equals space 0.
    94 Views
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    29. In the following, verify that the given functions, (explicit or implicit) is a solution of the corresponding differential equation:
    straight y space equals space straight e to the power of straight x plus 1                    :    straight y to the power of straight n minus straight y apostrophe space equals space 0
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    30. In the following, verify that the given functions, (explicit or implicit) is a solution of the corresponding differential equation:
    straight y space equals space straight x squared plus 2 straight x plus straight C                              :     straight y apostrophe minus 2 straight x minus 2 space equals space 0
                        
    97 Views
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