I'm trying to calculate this differential equation using implicit differentiation for (dy)/(dx) in terms of x and y: 2x3y+5x+6y−sin(πy)=8

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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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A. 4.2
B. 4.4
C. 4.7
D. 5.1

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