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Consider the differential equation 3y"( x ) + 27 y ( x )= 0 with initial conditions y(0) = 0 and y '(0) = 2000. The value of y at x = 1 is ________.
Correct answer is between '93,95'. Can you explain this answer?
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Consider the differential equation 3y"( x ) + 27 y ( x )= 0 with i...
3y"(x)+27y(x) = 0 , y(0) = 0 , y'(0) = 2000
Auxillary equation, 3m2 + 27 = 0
⇒m2+ 9 = 0 ⇒m = 0 +3i
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Consider the differential equation 3y"( x ) + 27 y ( x )= 0 with i...
Given Differential Equation
3y(x) + 27y'(x) = 0
Initial Conditions
y(0) = 0
y'(0) = 2000
Solution
To solve this differential equation, we first rewrite it in the standard form:
y'(x) + 9y(x) = 0
This is a first-order linear differential equation with constant coefficients. The solution to this type of equation is of the form y(x) = Ce^(-9x), where C is a constant.
Applying the initial condition y(0) = 0, we get:
0 = Ce^0
C = 0
Therefore, the solution to the differential equation is y(x) = 0.
Next, we need to find the value of y at x = 1. Substituting x = 1 into the solution:
y(1) = 0
Therefore, the value of y at x = 1 is 0.
Conclusion
The value of y at x = 1 is 0.
3y(x) + 27y'(x) = 0
Initial Conditions
y(0) = 0
y'(0) = 2000
Solution
To solve this differential equation, we first rewrite it in the standard form:
y'(x) + 9y(x) = 0
This is a first-order linear differential equation with constant coefficients. The solution to this type of equation is of the form y(x) = Ce^(-9x), where C is a constant.
Applying the initial condition y(0) = 0, we get:
0 = Ce^0
C = 0
Therefore, the solution to the differential equation is y(x) = 0.
Next, we need to find the value of y at x = 1. Substituting x = 1 into the solution:
y(1) = 0
Therefore, the value of y at x = 1 is 0.
Conclusion
The value of y at x = 1 is 0.
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Consider the differential equation 3y"( x ) + 27 y ( x )= 0 with initial conditions y(0) = 0 and y '(0) = 2000. The value of y at x = 1 is ________.Correct answer is between '93,95'. Can you explain this answer?
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