Solve the following differential equation: from Mathematics Dif
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    Differential Equations

    Multiple Choice QuestionsLong Answer Type

    261.

    Find one-parameter families of solution curves of the following differential equation:
    left parenthesis 1 plus straight x squared right parenthesis space dy space plus space 2 xy space dx space equals space cot space straight x space dx space space space space left parenthesis straight x not equal to 0 right parenthesis
      

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    Answer
    262.

    Find one-parameter families of solution curves of the following differential equation:
               straight x dy over dx plus straight y minus straight x plus straight x space straight y space cot space straight x space equals space 0 space space space left parenthesis straight x not equal to 0 right parenthesis

      

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    Answer
    263.

    Solve:  open parentheses fraction numerator straight e to the power of negative 2 square root of straight x end exponent over denominator square root of straight x end fraction minus fraction numerator straight y over denominator square root of straight x end fraction close parentheses dx over dy equals 1 comma space space space straight x not equal to space 0.

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    264. Solve the following differential equation:
    dy over dx space plus 2 space straight y space tan space straight x space equals space sin space straight x

    The given differential equation is
                     dy over dx plus 2 space straight y space tanx space equals space sin space straight x
    Comparing it with dy over dx plus Py space equals space straight Q comma we get,
                       straight P space equals space 2 space tanx space space space straight Q space equals space sin space straight x
    therefore space space space space integral straight P space dx space equals space 2 space integral space tan space straight x space dx space equals space minus 2 space log space cosx space space equals space log space left parenthesis cosx right parenthesis squared
    therefore space space space space space space space space space space straight I. straight F. space equals space straight e to the power of integral straight P space dx end exponent space equals space straight e to the power of log space left parenthesis cosx space right parenthesis to the power of negative 2 end exponent end exponent space equals space left parenthesis cos space straight x right parenthesis to the power of negative 2 end exponent space equals space fraction numerator 1 over denominator cos squared straight x end fraction
    therefore space space space space space space solution space of space differential space equation space is
                               straight y. space fraction numerator 1 over denominator cos squared straight x end fraction space equals space integral sin space straight x. space space fraction numerator 1 over denominator cos squared straight x end fraction dx plus straight c

                                              open square brackets therefore space space space straight y space straight e to the power of integral straight P space dx end exponent space equals space integral straight Q space straight e to the power of integral straight P space dx end exponent dx plus straight c close square brackets

    or                 fraction numerator straight y over denominator cos squared straight x end fraction space equals space integral space tanx space secx space dx plus straight c
    or           fraction numerator straight y over denominator cos squared straight x end fraction space equals space secx plus straight c
    or           straight y equals cosx plus straight c space cos squared straight x
    which is required solution. 
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    265. For the differential equation, find the general solution:
    dy over dx plus 2 straight y space equals sin space straight x
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    266. Solve the following differential equation:
    sin space straight x space dy over dx plus straight y space cosx space equals space cos space straight x space sin squared straight x
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    Multiple Choice QuestionsShort Answer Type

    267. Find a one parameter family of solutions of each of the following differential equation:
    straight y apostrophe cos squared straight x space equals space tanx minus space straight y
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    268. Find a one parameter family of solutions of each of the following differential equation:
                                 dy over dx equals negative fraction numerator straight x plus straight y space cosx over denominator 1 plus sinx end fraction
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    Multiple Choice QuestionsLong Answer Type

    269.

    Solve:
    straight y apostrophe minus 2 straight y space equals space cos space 3 straight x

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    Answer

    Multiple Choice QuestionsShort Answer Type

    270.

    Solve:
    straight y apostrophe plus straight y space equals space sin space straight x

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    Answer
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