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Q. The solution of the differential equation `dy/dx` `= (1 + x)(1 + y^2)` is A) `y=...

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user8235304 | Student, Grade 11 | Valedictorian

Posted July 5, 2013 at 5:53 PM via web

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Q. The solution of the differential equation `dy/dx` `= (1 + x)(1 + y^2)` is

A) `y= tan(x^2 + x + c)`

B)`y=tan(2x^2 + x + c)`

C)`y=tan(x^2 - x + c)`

D)`y=tan(x^2/2 + x + c)`

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted July 5, 2013 at 6:02 PM (Answer #1)

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The function has to be determined for which the differential equation `dy/dx = (1+x)(1+y^2)` holds.

It can be seen that the function should be such that the term (1+x) can be factored from the expression for `dy/dx` .

The rule for differentiation of nested functions has to be used for all the given options. But only for `y = tan(x^2/2 + x + c)` the derivative of `(x^2/2 + x + c)` is equal to x + 1

The correct answer is D, `y = tan(x^2/2+x+c)`

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