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y(x) = x-3/2 is a solution to 4x2 y′′ + 12xy′ + 3y = 0 , y (4) = 1/8 , and y'(4) = -3/64
Solution: As we noticed in previous illustration the function is a solution and we can after that notice that:
And therefore this solution also meets the initial conditions of y (4) = 1/8 , and y'(4) = -3/64.
Actually, y (x) = x-3/2 is the merely solution to this differential equation which satisfies such two initial conditions.
Determine the Projection of b = (2, 1, -1) onto a = (1, 0, -2) There is a requirement of a dot product and the magnitude of a. a → • b → = 4 ||a
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If z=re i ? ,find the value of |e iz | Solution) z=r(cos1+isin1) |e iz |=|e ir(cos1+isin1) |=|e -rsin1 |=e -rsin1
We have seen that if y is a function of x, then for each given value of x, we can determine uniquely the value of y as per the functional relationship. For some f
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So far we have considered differentiation of functions of one independent variable. In many situations, we come across functions with more than one independent variable
1+1
2 1/3 + 3 3/8
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for what k, q.p. kx2-8x+k can be factored into real linear factors. kx2-8x+k
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