Solve 3x 7y=x - ScanMath

Question

Solve the equation

Solve for x

Solve for y

x = 0

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Testing for symmetry about the origin

Testing for symmetry about the x-axis

Testing for symmetry about the y-axis

Not symmetry with respect to the origin

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r = 0 r = \frac{csc ( θ )}{21}

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Find the derivative with respect to x

Find the derivative with respect to y

\frac{d y}{d x} = \frac{1 - 21 y}{21 x}

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Find the second derivative with respect to x

Find the second derivative with respect to y

\frac{d ^{2} y}{d x ^{2}} = \frac{- 2 + 42 y}{21 x ^{2}}

Calculate

3 x 7 y = x

Simplify the expression

21 x y = x

Take the derivative of both sides

\frac{d}{d x} (21 x y) = \frac{d}{d x} (x)

Calculate the derivative

More Steps

21 y + 21 x \frac{d y}{d x} = \frac{d}{d x} (x)

Use \frac{d}{d x} x^{n} = n x^{n - 1} to find derivative

21 y + 21 x \frac{d y}{d x} = 1

Move the expression to the right-hand side and change its sign

21 x \frac{d y}{d x} = 1 - 21 y

Divide both sides

\frac{21 x \frac{d y}{d x}}{21 x} = \frac{1 - 21 y}{21 x}

Divide the numbers

\frac{d y}{d x} = \frac{1 - 21 y}{21 x}

Take the derivative of both sides

\frac{d}{d x} (\frac{d y}{d x}) = \frac{d}{d x} (\frac{1 - 21 y}{21 x})

Calculate the derivative

\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (\frac{1 - 21 y}{21 x})

Use differentiation rules

\frac{d ^{2} y}{d x ^{2}} = \frac{\frac{d}{d x} ( 1 - 21 y ) \times 21 x - ( 1 - 21 y ) \times \frac{d}{d x} ( 21 x )}{( 21 x ) ^{2}}

Calculate the derivative

More Steps

\frac{d ^{2} y}{d x ^{2}} = \frac{- 21 \frac{d y}{d x} \times 21 x - ( 1 - 21 y ) \times \frac{d}{d x} ( 21 x )}{( 21 x ) ^{2}}

Calculate the derivative

More Steps

\frac{d ^{2} y}{d x ^{2}} = \frac{- 21 \frac{d y}{d x} \times 21 x - ( 1 - 21 y ) \times 21}{( 21 x ) ^{2}}

Calculate

\frac{d ^{2} y}{d x ^{2}} = \frac{- 441 \frac{d y}{d x} \times x - ( 1 - 21 y ) \times 21}{( 21 x ) ^{2}}

Calculate

More Steps

\frac{d ^{2} y}{d x ^{2}} = \frac{- 441 \frac{d y}{d x} \times x - ( 21 - 441 y )}{( 21 x ) ^{2}}

Calculate

More Steps

\frac{d ^{2} y}{d x ^{2}} = \frac{- 441 x \frac{d y}{d x} - 21 + 441 y}{( 21 x ) ^{2}}

Calculate

More Steps

\frac{d ^{2} y}{d x ^{2}} = \frac{- 441 x \frac{d y}{d x} - 21 + 441 y}{441 x ^{2}}

Calculate

\frac{d ^{2} y}{d x ^{2}} = \frac{- 21 x \frac{d y}{d x} - 1 + 21 y}{21 x ^{2}}

Use equation \frac{d y}{d x} = \frac{1 - 21 y}{21 x} to substitute

\frac{d ^{2} y}{d x ^{2}} = \frac{- 21 x \times \frac{1 - 21 y}{21 x} - 1 + 21 y}{21 x ^{2}}

Solution

More Steps

\frac{d ^{2} y}{d x ^{2}} = \frac{- 2 + 42 y}{21 x ^{2}}

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