Calculus Examples

$\frac{d y}{d t} = 0$

Step 1

Rewrite the equation.

$d y = 0 d t$

Step 2

Integrate both sides.

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Step 2.1

Set up an integral on each side.

$\int d y = \int 0 d t$

Step 2.2

Apply the constant rule.

$y + C_{1} = \int 0 d t$

Step 2.3

Integrate the right side.

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Step 2.3.1

The integral of $0$ with respect to $t$ is $0$ .

$y + C_{1} = 0 + C_{2}$

Step 2.3.2

Add $0$ and $C_{2}$ .

$y + C_{1} = C_{2}$

Step 2.4

Group the constant of integration on the right side as $D$ .

$y = D$