Solve the following differential equation: from Mathematics Dif
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    Differential Equations

    Multiple Choice QuestionsShort Answer Type

    101. Find a one-parameter family of solutions of the following differential equation, indicating carefully the interval in which the solutions are valid:
    straight e to the power of straight y dx plus straight e to the power of straight x dy space equals space 0
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    102. Find a one-parameter family of solutions of the following differential equation, indicating carefully the interval in which the solutions are valid:
    left parenthesis sinx plus cosx right parenthesis space dy space equals space left parenthesis cosx minus sinx right parenthesis space dx
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    103. Find a one-parameter family of solutions of the following differential equation, indicating carefully the interval in which the solutions are valid:
    straight y apostrophe space equals left parenthesis 1 plus straight x squared right parenthesis thin space left parenthesis 1 plus straight y squared right parenthesis
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    104. Find a one-parameter family of solutions of the following differential equation, indicating carefully the interval in which the solutions are valid:
    left parenthesis straight e to the power of straight x plus straight e to the power of straight x right parenthesis space dy space minus space left parenthesis straight e to the power of straight x minus straight e to the power of straight x right parenthesis space dx space equals space 0
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    105.

    Solve the differential equation
    left parenthesis tan squared straight x plus 2 space tanx space plus 5 right parenthesis space dy over dx space equals space 2 left parenthesis 1 plus tanx right parenthesis space sec squared straight x.

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    106. Solve the following differential equation:
    x cos y dy = (x ex log x + ex) dx.
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    107. Solve the following differential equation:
    dy over dx space equals space log space left parenthesis straight x plus 1 right parenthesis

    The given differential equation is
                          dy over dx space equals space log space left parenthesis straight x plus 1 right parenthesis
    Separating the variables, we get,
                            dy space equals space log space left parenthesis straight x plus 1 right parenthesis. space dx
    Integrating,       integral dy space equals space integral log space left parenthesis straight x plus 1 right parenthesis. space 1 space dx
    therefore space space space space space space space space space space space straight y space equals space log space left parenthesis straight x plus 1 right parenthesis space. straight x space space minus space integral fraction numerator 1 over denominator straight x plus 1 end fraction straight x space dx

    or            straight y equals straight x space log left parenthesis straight x plus 1 right parenthesis minus space integral fraction numerator left parenthesis straight x plus 1 right parenthesis space minus space 1 over denominator straight x plus 1 end fraction dx

    or            straight y space equals straight x space log space left parenthesis straight x plus 1 right parenthesis space minus space integral open parentheses 1 minus fraction numerator 1 over denominator straight x plus 1 end fraction close parentheses dx

    or           straight y equals straight x space log space left parenthesis straight x plus 1 right parenthesis space minus space open square brackets straight x minus log left parenthesis straight x plus 1 right parenthesis close square brackets plus straight c

    or          straight y equals space straight x space log space left parenthesis straight x plus 1 right parenthesis space minus space straight x space plus space log space left parenthesis straight x plus 1 right parenthesis space plus straight c
    or           straight y equals left parenthesis straight x plus 1 right parenthesis space log space left parenthesis straight x plus 1 right parenthesis space minus straight x space plus straight c
    which is required solution. 
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    108. Solve the following differential equation:
                left parenthesis straight y plus straight x space straight y right parenthesis space dx space plus space left parenthesis straight x minus straight x space straight y squared right parenthesis space dy space equals space 0
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    109. Solve the following differential equation:
    left parenthesis 1 minus straight x squared right parenthesis space dy space plus space straight x space straight y space dx space equals space straight x space straight y squared space dx.
                
    94 Views
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    110. Solve the following differential equation:
    dy over dx space equals space 1 plus straight x plus straight y plus xy comma space space straight y greater than 0

                
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    Answer
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