What are the solutions to the equation solvefor x,d(x)=xdt(x) ?

The solutions to the equation solvefor x,d(x)=xdt(x) are x=0,x= 1/t ;\quad t\ne 0,d\ne 0

Find the zeros of solvefor x,d(x)=xdt(x)

The zeros of solvefor x,d(x)=xdt(x) are x=0,x= 1/t ;\quad t\ne 0,d\ne 0

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solve for

x, d (x) = x d t (x)

x = 0, x = \frac{1}{t}; t \neq = 0, d \neq = 0

Solution steps

d (x) = x d t (x)

Move

x d t (x)

to the left side

d x - x d t x = 0

Factor

d x - x d t x : d x (1 - x t)

d x (1 - x t) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 1 - x t = 0

Solve

1 - x t = 0 : x = \frac{1}{t}; t \neq = 0

The solutions to the quadratic equation are:

x = 0, x = \frac{1}{t}; t \neq = 0, d \neq = 0

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - 2 y = 3 e^{2 x} - x^{2}

\frac{d ^{2} y}{d x ^{2}} + 4 y = sin (x) cos (x)

y^{^{'''}} + y^{^{'}} = sec (t), y (0) = 3, y^{^{''}} (0) = - 2

y^{^{''}} + 36 y = cos (4 x)

\frac{d ^{2} y}{d x ^{2}} + y = x sin (2 x)

What are the solutions to the equation solvefor x,d(x)=xdt(x) ?
The solutions to the equation solvefor x,d(x)=xdt(x) are x=0,x= 1/t ;\quad t\ne 0,d\ne 0
Find the zeros of solvefor x,d(x)=xdt(x)
The zeros of solvefor x,d(x)=xdt(x) are x=0,x= 1/t ;\quad t\ne 0,d\ne 0