(d^2y)/(dx^2)=4e^{-x},y(0)=3,y^'(0)=2

解答

\frac{d ^{2} y}{d x ^{2}} = 4 e^{- x}, y (0) = 3, y^{^{'}} (0) = 2

y = 4 e^{- x} + 6 x - 1

求解步骤

y^{''} (x) = 4 e^{- x}

解

y^{''} (x) = 4 e^{- x} : y^{'} (x) = - 4 e^{- x} + c_{1}

解

y^{'} (x) = - 4 e^{- x} + c_{1} : y = 4 e^{- x} + c_{1} x + c_{2}

应用初始条件:

y = 4 e^{- x} + 6 x - 1

y = 4 e^{- x} + 6 x - 1

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