The general solution of is

MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations

Problem

The general solution of y′′−y=0y''-y=0 is y=C1ex+C2e−xy=C_1e^{x}+C_2e^{-x}. Find the particular solution satisfying y(0)=3y(0)=3 and having a horizontal tangent at x=0x=0. (a) y=2ex+e−xy=2e^{x}+e^{-x} (b) y=32(ex+e−x)y=\dfrac{3}{2}\left(e^{x}+e^{-x}\right) (c) y=32(ex−e−x)y=\dfrac{3}{2}\left(e^{x}-e^{-x}\right) (d) y=3exy=3e^{x}

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