(32u^7-16u^5)/(4u^3)

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Solution for (32u^7-16u^5)/(4u^3) equation: 


D( u )

4*u^3 = 0

4*u^3 = 0

4*u^3 = 0

4*u^3 = 0 // : 4

u^3 = 0

u = 0

u in (-oo:0) U (0:+oo)

(32*u^7-(16*u^5))/(4*u^3) = 0

(32*u^7-16*u^5)/(4*u^3) = 0

32*u^7-16*u^5 = 0

16*u^5*(2*u^2-1) = 0

2*u^2 = 1 // : 2

u^2 = 1/2

u^2 = 1/2 // ^ 1/2

abs(u) = (1/2)^(1/2)

u = (1/2)^(1/2) or u = -(1/2)^(1/2)

16*u^5*(u-(1/2)^(1/2))*(u+(1/2)^(1/2)) = 0

(16*u^5*(u-(1/2)^(1/2))*(u+(1/2)^(1/2)))/(4*u^3) = 0

( 16*u^5 )

16*u^5 = 0 // : 16

u^5 = 0

u = 0

( u+(1/2)^(1/2) )

u+(1/2)^(1/2) = 0 // - (1/2)^(1/2)

u = -(1/2)^(1/2)

( u-(1/2)^(1/2) )

u-(1/2)^(1/2) = 0 // + (1/2)^(1/2)

u = (1/2)^(1/2)

u in { 0} 

u in { -(1/2)^(1/2), (1/2)^(1/2) }

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