What are the solutions to the equation d(x^3)=dx ?

The solutions to the equation d(x^3)=dx are x=0,x=-1,x=1;\quad d\ne 0

Find the zeros of d(x^3)=dx

The zeros of d(x^3)=dx are x=0,x=-1,x=1;\quad d\ne 0

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d (x^{3}) = d x

x = 0, x = - 1, x = 1; d \neq = 0

Solution steps

d (x^{3}) = d x

Move

d x

to the left side

d x^{3} - d x = 0

Factor

d x^{3} - d x : d x (x + 1) (x - 1)

d x (x + 1) (x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x + 1 = 0 or x - 1 = 0

Solve

x + 1 = 0 : x = - 1

Solve

x - 1 = 0 : x = 1

The solutions are

x = 0, x = - 1, x = 1; d \neq = 0

y^{^{''}} + 4 y = 2 sin (2 t) + t

y^{^{''}} + 9 y^{^{'}} + 14 y = e^{- x}

y^{^{''}} - y^{^{'}} = - 3 x^{2}

d, d (t) = 5 t^{2} + 10 - 12

\frac{d ^{2} y}{d x ^{2}} - 9 y = 54

What are the solutions to the equation d(x^3)=dx ?
The solutions to the equation d(x^3)=dx are x=0,x=-1,x=1;\quad d\ne 0
Find the zeros of d(x^3)=dx
The zeros of d(x^3)=dx are x=0,x=-1,x=1;\quad d\ne 0