SOLUTION: Solve the following initial value problems:
A)x"+x=0 :x(0)=0,x'(0)=1
b)x"+4x=0; x(0)=1, x'(0)=0
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-> SOLUTION: Solve the following initial value problems:
A)x"+x=0 :x(0)=0,x'(0)=1
b)x"+4x=0; x(0)=1, x'(0)=0
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You can put this solution on YOUR website! A) We can let . This gives , and . Then . This implies that , from the given DE. Since we don't want A = 0, then B = 1. (We can drop B = -1 without loss of generality.)
So . From the initial value x'(0) = 1, we get A = 1. Therefore .
B) The solution of this IVP follows along the same line as above, but this time we let. By using the differential equation we get B=2, and by using the initial condition, we get A = 1. Therefore .
