Solve 2x y=13x - ScanMath

Question

Solve the equation

Solve for x

Solve for y

x = 0

Show Solution

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

Show Solution

r = 0 r = \frac{13 csc ( θ )}{2}

Show Solution

Find the derivative with respect to x

Find the derivative with respect to y

\frac{d y}{d x} = \frac{13 - 2 y}{2 x}

Show Solution

Find the second derivative with respect to x

Find the second derivative with respect to y

\frac{d ^{2} y}{d x ^{2}} = \frac{- 13 + 2 y}{x ^{2}}

Calculate

2 x y = 13 x

Take the derivative of both sides

\frac{d}{d x} (2 x y) = \frac{d}{d x} (13 x)

Calculate the derivative

More Steps

2 y + 2 x \frac{d y}{d x} = \frac{d}{d x} (13 x)

Calculate the derivative

More Steps

2 y + 2 x \frac{d y}{d x} = 13

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

2 x \frac{d y}{d x} = 13 - 2 y

Divide both sides

\frac{2 x \frac{d y}{d x}}{2 x} = \frac{13 - 2 y}{2 x}

Divide the numbers

\frac{d y}{d x} = \frac{13 - 2 y}{2 x}

Take the derivative of both sides

\frac{d}{d x} (\frac{d y}{d x}) = \frac{d}{d x} (\frac{13 - 2 y}{2 x})

Calculate the derivative

\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (\frac{13 - 2 y}{2 x})

Use differentiation rules

\frac{d ^{2} y}{d x ^{2}} = \frac{\frac{d}{d x} ( 13 - 2 y ) \times 2 x - ( 13 - 2 y ) \times \frac{d}{d x} ( 2 x )}{( 2 x ) ^{2}}

Calculate the derivative

More Steps

\frac{d ^{2} y}{d x ^{2}} = \frac{- 2 \frac{d y}{d x} \times 2 x - ( 13 - 2 y ) \times \frac{d}{d x} ( 2 x )}{( 2 x ) ^{2}}

Calculate the derivative

More Steps

\frac{d ^{2} y}{d x ^{2}} = \frac{- 2 \frac{d y}{d x} \times 2 x - ( 13 - 2 y ) \times 2}{( 2 x ) ^{2}}

Calculate

\frac{d ^{2} y}{d x ^{2}} = \frac{- 4 \frac{d y}{d x} \times x - ( 13 - 2 y ) \times 2}{( 2 x ) ^{2}}

Calculate

More Steps

\frac{d ^{2} y}{d x ^{2}} = \frac{- 4 \frac{d y}{d x} \times x - ( 26 - 4 y )}{( 2 x ) ^{2}}

Calculate

More Steps

\frac{d ^{2} y}{d x ^{2}} = \frac{- 4 x \frac{d y}{d x} - 26 + 4 y}{( 2 x ) ^{2}}

Calculate

More Steps

\frac{d ^{2} y}{d x ^{2}} = \frac{- 4 x \frac{d y}{d x} - 26 + 4 y}{4 x ^{2}}

Calculate

\frac{d ^{2} y}{d x ^{2}} = \frac{- 2 x \frac{d y}{d x} - 13 + 2 y}{2 x ^{2}}

Use equation \frac{d y}{d x} = \frac{13 - 2 y}{2 x} to substitute

\frac{d ^{2} y}{d x ^{2}} = \frac{- 2 x \times \frac{13 - 2 y}{2 x} - 13 + 2 y}{2 x ^{2}}

Solution

More Steps

\frac{d ^{2} y}{d x ^{2}} = \frac{- 13 + 2 y}{x ^{2}}

Show Solution