What is the general solution for solvefor x,arccot(x^2)y=arccot(x^2) ?

The general solution for solvefor x,arccot(x^2)y=arccot(x^2) is No Solution for x\in\mathbb{R}

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solvefor x,arccot(x^2)y=arccot(x^2)

solve for

x, arccot (x^{2}) y = arccot (x^{2})

No Solution for x \in R

Solution steps

arccot (x^{2}) y = arccot (x^{2})

Solve by substitution

arccot (x^{2}) y = arccot (x^{2})

Let:

arccot (x^{2}) = u

u y = u

u y = u : u = 0

u y = u

Move

u

to the left side

u y = u

Subtract

u

from both sides

u y - u = u - u

Simplify

u y - u = 0

u y - u = 0

Factor

u y - u : u (y - 1)

u y - u

Factor out common term

u

= u (y - 1)

u (y - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

u = 0

Substitute back

u = arccot (x^{2})

arccot (x^{2}) = 0

arccot (x^{2}) = 0

arccot (x^{2}) = 0 :

No Solution

arccot (x^{2}) = 0

0 < arccot (x) < π

No Solution

Combine all the solutions

No Solution for x \in R

\frac{50}{33} = \frac{sin ( x )}{sin ( 12 0 ^{\circ} - x )}

cot (x) csc (x) = cos (x)

2 tan (x) = 2

0.5 = cos (\frac{π}{6} x)

cos^{2} (x) = \frac{π}{4}

What is the general solution for solvefor x,arccot(x^2)y=arccot(x^2) ?
The general solution for solvefor x,arccot(x^2)y=arccot(x^2) is No Solution for x\in\mathbb{R}