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(1 point) Find y as a function of x if y(x) = -2sin(2x)+7cos(2x)+8

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y+4y0 A linear homogeneous ODE with constant coefficients has the form of For an equation a,++a,y+a,y-0, assume a solution of the form y -e. So, y+4y0 So, e(+4)-o So, the general solution of the one real root and two complex root has taken the form is So, y ZGeor+/r (c, cos(2x)-G sin(2x)) So, y-c+ccos(2x)+c,sin(2x) Sincc, y(0)-2 So, y(0)-c+c,cos (2.(0))+c, sin(2.(0) Put G--2-G in yZG +c, cos(2x) +G sin (2x) So, y-2-G +c, cos(2x)+G sin(2x) Now y(0)-14 -2c, sin (2x)+2c, cos(2x So, y(0)-2c,sin (2.0)+2c, cos(2.0)So, -14-2c,;c,7 Put c 7 in y+cos(2x)+c, sin(21) So, y--2-c2tGcos(2x)-7sin(2x) Now y(0)-0 So, y(o)-4c, cos(20)+28sin(2.0) So, 0--4c, So, G20 Put c, -0 in y 2-+, cos(2x)-7sin(2x) So, -2-7sin(2x)

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