Solve the following differential equation:             f
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    Differential Equations

    Multiple Choice QuestionsShort Answer Type

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    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

                

    The given differential equation is
                         left parenthesis straight x squared straight y plus straight x squared right parenthesis space dx plus left parenthesis straight x space straight y squared minus straight y squared right parenthesis space dy space equals space 0
    or             straight x squared left parenthesis straight y plus 1 right parenthesis space dx plus space straight y squared left parenthesis straight x minus 1 right parenthesis space dy space equals space 0 space space space space or space space space space straight y squared left parenthesis straight x minus 1 right parenthesis space dy space equals space minus straight x squared left parenthesis straight y plus 1 right parenthesis space dx
    Separating the variables, we get,
                       fraction numerator straight y squared over denominator straight y plus 1 end fraction dy space equals space minus fraction numerator straight x squared over denominator straight x minus 1 end fraction dxaa
    Integrating,  integral fraction numerator straight y squared over denominator straight y plus 1 end fraction dy space equals space minus integral fraction numerator straight x squared over denominator straight x minus 1 end fraction dx
    therefore space space space space integral open parentheses straight y minus 1 plus fraction numerator 1 over denominator straight y plus 1 end fraction close parentheses space dy space equals space minus integral open parentheses straight x plus 1 plus fraction numerator 1 over denominator straight x minus 1 end fraction close parentheses dx therefore space space space straight y squared over 2 minus straight y plus log space open vertical bar straight y plus 1 close vertical bar space equals space open square brackets straight x squared over 2 plus straight x plus log space open vertical bar straight x minus 1 close vertical bar close square brackets space plus space straight c
    which is required solution.
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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
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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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    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
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    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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    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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