Solve ds^2=dr^2-c^2dt^2

Evaluate

d s^{2} = d r^{2} - c^{2} d t^{2}

Rewrite the expression

d s^{2} = d r^{2} - d t^{2} c^{2}

Swap the sides of the equation

d r^{2} - d t^{2} c^{2} = d s^{2}

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

- d t^{2} c^{2} = d s^{2} - d r^{2}

Divide both sides

\frac{- d t ^{2} c ^{2}}{- d t ^{2}} = \frac{d s ^{2} - d r ^{2}}{- d t ^{2}}

Divide the numbers

c^{2} = \frac{d s ^{2} - d r ^{2}}{- d t ^{2}}

Divide the numbers

More Steps

c^{2} = \frac{- s ^{2} + r ^{2}}{t ^{2}}

Take the root of both sides of the equation and remember to use both positive and negative roots

c = \pm \frac{- s ^{2} + r ^{2}}{t ^{2}}

Simplify the expression

More Steps

c = \pm \frac{- s ^{2} + r ^{2}}{∣ t ∣}

Solution

c = \frac{- s ^{2} + r ^{2}}{∣ t ∣} c = - \frac{- s ^{2} + r ^{2}}{∣ t ∣}

Solve the equation