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Persamaan diferensial takhomogen berikut

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$y\"+y'-6y+6x^2-2x-8=0$

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dengan

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$y(0)=2$ dan $y'(0)=1$

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diketahui memiliki solusi berbentuk $y(x)=Ae^{Bx}+Ce^{Dx}+Ex^2+Fx+G$.

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Nilai dari $A+B+C+D+E+F+G$ adalah

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