For which ordered pair does the function satisfy the differential equation ?

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

For which ordered pair (a,b)(a,b) does the function y(x)=(x2+ax+b) exy(x)=(x^{2}+a x+b)\,e^{x} satisfy the differential equation dydx=(x2+4x+5) ex\dfrac{dy}{dx}=(x^{2}+4x+5)\,e^{x}? (a) (2,5)(2,5) (b) (4,5)(4,5) (c) (2,3)(2,3) (d) (3,2)(3,2)

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