Solve the differential equation from Mathematics Differential
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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.

    The given differential equation is
                    open parentheses tan squared straight x plus 2 space tan space straight x plus 5 close parentheses space dy over dx space equals space 2 left parenthesis 1 minus tanx right parenthesis space sec squared straight x
    or        dy over dx equals space fraction numerator 2 space sec squared straight x plus 2 space tanx space sec squared straight x over denominator tan squared straight x plus 2 space tanx plus 5 end fraction
    Separating the variables,  we get,         
                          dy space equals space fraction numerator 2 space tanx space sec squared straight x space plus space 2 space sec squared straight x over denominator tan squared straight x plus 2 space tan space straight x plus 5 end fraction dx
    Integrating ,   integral 1 space dy space equals space integral fraction numerator 2 space tanx space sec squared straight x space plus space 2 sec squared straight x over denominator tan squared straight x plus 2 space tan space straight x plus 5 end fraction dx
    therefore space space space space space space space space space space space straight y equals log space open vertical bar tan squared straight x plus 2 tanx plus 5 close vertical bar space plus straight c 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 open square brackets because space space integral fraction numerator straight f apostrophe left parenthesis straight x right parenthesis over denominator straight f left parenthesis straight x right parenthesis end fraction dx space equals space log space open vertical bar straight f left parenthesis straight x right parenthesis close vertical bar close square brackets
    which is the required solution. 
     
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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
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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
    86 Views
    Answer
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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
    Answer
    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

                
    85 Views
    Answer
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