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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.
Find out the domain of each of the following. (a) f (x,y) = √ (x+y) (b) f (x,y) = √x+√y (c) f (x,y) = ln (9 - x 2 - 9y 2 ) Solution (a) In this example we know
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(3+x)(3-x)
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