answer to a: Ygs =Ae^-2x + Be^-3x +3x^2 -4x
im not sure how to do b please help thanks
\(y = A e^{-2x}+Be^{-3x} + 3x^2 - 4x\\ \dfrac{dy}{dx} = -2A e^{-2x} -3Be^{-3x} + 6x-4\\ \left . \dfrac{dy}{dx}\right|_{x=0} = -2A -3B - 4 = 7\\ y(0) = A + B = 4\\ -2A -3B = 11\\ A+B = 4\\ \text{I leave you to solve for $A,~B$}\)
thank you rom.
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