Find the general solution of each of the following equations: f
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    Differential Equations

    Multiple Choice QuestionsShort Answer Type

    111. Solve the following differential equation:
    open parentheses straight x squared straight y plus straight x squared close parentheses space dx space plus space left parenthesis straight x space straight y squared minus straight y squared right parenthesis space dy space equals space 0

                
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    112. Solve the following differential equation:
    straight y left parenthesis 1 minus straight x squared right parenthesis dy over dx space equals space straight x left parenthesis 1 plus straight y squared right parenthesis


                
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    113. Find the general solution of each of the following equations
    dy over dx equals straight x to the power of 5 plus straight x squared minus 2 over straight x
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    114. Find the general solution of each of the following equations:
    left parenthesis straight x plus 2 right parenthesis space dy over dx space equals space straight x squared plus 4 straight x minus 9

    The given differential equation is
                 left parenthesis straight x plus 2 right parenthesis space dy over dx space equals space straight x squared plus 4 straight x minus 9    or    dy over dx space equals space fraction numerator straight x squared plus 4 straight x minus 9 over denominator straight x plus 2 end fraction
    Separating the variables, we get
                               dy space equals space open parentheses fraction numerator straight x squared plus 4 straight x minus 9 over denominator straight x plus 2 end fraction close parentheses space dx
    or                 dy space equals open parentheses fraction numerator straight x squared plus 4 straight x minus 9 over denominator straight x plus 2 end fraction close parentheses dx
    or         dy space equals space open parentheses straight x plus 2 minus fraction numerator 13 over denominator straight x plus 2 end fraction close parentheses dx
    Integrating, 
                   straight y equals straight x squared over 2 plus 2 straight x minus 13 space log space open vertical bar straight x plus 2 close vertical bar space plus space straight c
    which is required solution. 
                                          straight x plus 2 space space fraction numerator straight x plus 2 over denominator long division enclose straight x squared plus 4 straight x minus 9 end enclose end fraction space space space space space space space space space space space space space space space space straight x squared plus 2 straight x space space space space space space space space space space space space space space space space minus space space minus space space space space space space space space space space space space space _________ space space space space space space space space space space space space space 2 straight x space space minus space 9 space space space space space space space space space space space space space 2 straight x space plus space 4 space space space space space space space space space space space space space space minus space space space space space space space space space space space space space _________ space space space space space space space space space space space space space space space space space space space space space space space space 13










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    115. Find the general solution of each of the following equations:
    dy over dx plus 2 straight x equals space straight e to the power of 3 straight x end exponent
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    Answer
    116. Find the general solution of each of the following equations:
    dy over dx equals fraction numerator straight y left parenthesis straight x squared minus 1 right parenthesis over denominator straight x left parenthesis straight y squared minus 1 right parenthesis end fraction
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    117. Find the general solution of each of the following equation:
    left parenthesis straight x minus 1 right parenthesis space straight y apostrophe space equals space 2 space straight x cubed space straight y space where space straight y apostrophe space equals space dy over dx
    86 Views
    Answer
    118. Find the general solution of the differential equation:
    dy over dx plus square root of fraction numerator 1 minus straight y squared over denominator 1 minus straight x squared end fraction end root space equals space 0.
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    Answer
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    119. Find a one parameter family of solutions of each of the following differential equation:
    y' = ex + y + e–x + y
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    120. Find a one parameter family of solutions of each of the following differential equation:
    y' = (cos2x – sin2x) cos2 y
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