Differential Equations Integrating y by x. This may be a bit of a silly questions, but when solving a differential equation by finding an integrating factor, is it possible to integrate a function of y and x by x? I understand that in multi variable calculus the y would be treated as a constant, but I am not sure why the same does not apply in differential equations. For example... For the differential equation y′+y=xy^3

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The solution of a differential equation y′′+3y′+2y=0 is of the form
A) $c_1{e}^x+c_2{e}^{2x}$
B) $c_1{e}^{-<!--\; -\; -->x}+c_2{e}^{3x}$
C) $c_1{e}^{-<!--\; -\; -->x}+c_2{e}^{-<!--\; -\; -->2x}$
D) $c_1{e}^{-<!--\; -\; -->2x}+c_2{2}^{-<!--\; -\; -->x}$

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Look at this series: 1.5, 2.3, 3.1, 3.9, ... What number should come next?
A. 4.2
B. 4.4
C. 4.7
D. 5.1

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The differential coefficient of $\sec \left({\tan }^{-1}\left(x\right)\right)$.