Find the general solution of the differential equation y dx –
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    Differential Equations

    Multiple Choice QuestionsLong Answer Type

    281. Find the general solution of the following differential equation:
    dy over dx plus fraction numerator 4 straight x over denominator straight x squared plus 1 end fraction straight y space equals negative fraction numerator 1 over denominator left parenthesis straight x squared plus 1 right parenthesis cubed end fraction
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    Answer

    Multiple Choice QuestionsShort Answer Type

    282.

    Solve:  open parentheses straight x plus straight y close parentheses space dy over dx space equals space 1.

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    Multiple Choice QuestionsLong Answer Type

    283.

    Solve:
          open parentheses straight x plus 2 straight y cubed close parentheses space straight y apostrophe space equals space straight y comma space space straight y greater than 0

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    Answer

    Multiple Choice QuestionsShort Answer Type

    284.

    Solve:
    straight y space dx space plus space left parenthesis straight x minus straight y right parenthesis squared space dy space equals space 0
          

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    Multiple Choice QuestionsLong Answer Type

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    285. Find the general solution of the differential equation y dx – (x + 2 y2) dy = 0.

     The given differential equation is
           y dx – (x + 2 y2) dy = 0
     or    straight y dx over dy minus straight x minus 2 straight y squared space equals space 0 space space space space or space space space straight y dx over dy minus straight x space equals space 2 straight y squared
    or    dx over dy minus 1 over straight y straight x space equals space 2 straight y
    Comparing it with dx over dy plus Px space equals space straight Q comma space space we space get comma space space straight P space equals space minus 1 over straight y comma space space straight Q space equals space 2 straight y

    therefore space space space space integral space straight P space dy space equals space minus integral 1 over straight y dy space equals space minus log space straight y space space space space space space space space straight e to the power of integral straight P space dy end exponent space equals space straight e to the power of negative log space straight y end exponent space equals space straight e to the power of log space straight y to the power of negative 1 end exponent end exponent space equals space straight y to the power of negative 1 end exponent space equals space 1 over straight y
    Solution of differential equation is
                      xe to the power of integral straight P space dy end exponent space equals space integral straight Q space straight e to the power of integral straight P space dy end exponent dy space plus space straight c
    or       straight x. space 1 over straight y space equals space integral space 2 straight y. space 1 over straight y dy plus straight c
    or         straight x over straight y space equals space 2 space integral space 1 space dy space plus straight c space space space or space space space straight x over straight y space equals space 2 straight y plus straight c
    or      straight x equals space 2 straight y squared plus straight c space straight y space is space the space required space solution. space                
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    286. Solve the following differential equation:
    (1 + y2)dx = (tan– 1 y – x) dy
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    Answer
    287. Solve the following differential equation:
    square root of 1 minus straight y squared end root space dx equals left parenthesis sin to the power of negative 1 end exponent straight y space minus straight x right parenthesis space dy
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    Multiple Choice QuestionsShort Answer Type

    288. Find a one parameter family of solutions of each of the following differential equation e–y sec2 y dy = dx + x dy.
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    Multiple Choice QuestionsLong Answer Type

    289. Find the particular solution of the differential equation:
                         dy over dx plus straight y space cotx space equals space 2 straight x plus straight x squared space cotx space space space left parenthesis straight x not equal to 0 right parenthesis
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    Answer
    290. For the given differential equation, find a particular solution satisfying the given condition:
    dy over dx plus 2 straight y space tan space straight x space equals space sin space straight x space colon space straight y space space equals space 0 space space when space straight x space equals space straight pi over 3

                         
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