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  3. consider the ode y"+ 4 y'+ 4 y = 5 e^(? 2 x ). ( a

Consider the ODE y"+ 4 y'+ 4 y = 5 e^(? 2 x ). ( a)...

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Advance Math

Consider the ODE y"+ 4 y'+ 4 y = 5 e^(? 2 x ). (

a) Verify that y 1 ( x) = e ? 2 x and y 2 ( x) = xe ? 2 xsatisfy the corresponding homogeneous equation.

(b) Use the Superposition Principle, with appropriatecoefficients, to state the general solution y h ( x ) of thecorresponding homogeneous equation.

(c) Verify that y p ( x) = 52 x 2 e ? 2 x is a particularsolution to the given nonhomogeneous ODE.

(d) Use the Nonhomogeneous Principle to write the generalsolution y ( x ) to the nonhomogeneous ODE.

(e) Solve the IVP consisting of the nonhomogeneous ODE and theinitial conditions y(0) = 1 , y 0 (0) = ? 1 .

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