Note WeBWorK will interpret acos(x) as cos-1 (x), so in order to write a times c

Question

Note WeBWorK will interpret acos(x) as cos-1 (x), so in order to write a times cos(x) you need to type a * cos(x) or put a space between them. The general solution of the homogeneous differential equation y" +4y = 0 can be written as yc = a cos(2x) + b sin(2x) where a, b are arbitrary constants and is a particular solution of the nonhomogeneous equation y" +4y = 8e2^x By superposition, the general solution of the equation y" +4y = 8e^2x is NOTE: you must use a, b for the arbitrary constants. Find the solution satisfying the initial conditions y(0) = 1, y'(0) = 3 The fundamental theorem for linear IVPs shows that this solution is the unique solution to the IVP on the interval The Wronskian W of the fundamental set of solutions cos(2 x) and sin(2 x) of the homogeneous equation is

Explanation / Answer

y(x)=e2x+ a*cos(2x) +b*sin(2x)

y(0)=1 ==>a+1 =1 ==>a=0

y'(x)=2e2x+ -2a*sin(2x) +2b*cos(2x)

y'(0)=3

2b+2=3 ==>b=1/2

y=e2x+(1/2)*sin(2x)

y=e2x+ cosxsinx

interval(-infinity,infinity)

W=2

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