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A. show that Y1(x)=0and Y2(x)=x^3/2 are solutions for r>等於0of the differential equation Y'=(3/2)y^1/3
It is easy, for the differential equation:
y' = (3/2)y^(1/3)
For y1(x) = 0, y1'(x) = 0
Obviously, it satisfies both sides of the equation.
For y2(x) = x^(3/2), y2'(x) = (3/2)x^(1/2)
L.H.S. = (3/2)x^(1/2)
R.H.S. = (3/2)(x^(3/2))^(1/3) = (3/2)x^(1/2) = L.H.S.
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Verified answer
It is easy, for the differential equation:
y' = (3/2)y^(1/3)
For y1(x) = 0, y1'(x) = 0
Obviously, it satisfies both sides of the equation.
For y2(x) = x^(3/2), y2'(x) = (3/2)x^(1/2)
L.H.S. = (3/2)x^(1/2)
R.H.S. = (3/2)(x^(3/2))^(1/3) = (3/2)x^(1/2) = L.H.S.