Calculus Examples

$2 (8) (0.6) + 2 (6) \frac{d y}{d t} = 0$

Step 1

Separate the variables.

Tap for more steps...

Step 1.1

Solve for $\frac{d y}{d t}$ .

Tap for more steps...

Step 1.1.1

Simplify each term.

Tap for more steps...

Step 1.1.1.1

Multiply $2 (8) \cdot 0.6$ .

Tap for more steps...

Step 1.1.1.1.1

Multiply $2$ by $8$ .

$16 \cdot 0.6 + 2 (6) \frac{d y}{d t} = 0$

Step 1.1.1.1.2

Multiply $16$ by $0.6$ .

$9.6 + 2 (6) \frac{d y}{d t} = 0$

Step 1.1.1.2

Multiply $2$ by $6$ .

$9.6 + 12 \frac{d y}{d t} = 0$

Step 1.1.2

Subtract $9.6$ from both sides of the equation.

$12 \frac{d y}{d t} = - 9.6$

Step 1.1.3

Divide each term in $12 \frac{d y}{d t} = - 9.6$ by $12$ and simplify.

Tap for more steps...

Step 1.1.3.1

Divide each term in $12 \frac{d y}{d t} = - 9.6$ by $12$ .

$\frac{12 \frac{d y}{d t}}{12} = \frac{- 9.6}{12}$

Step 1.1.3.2

Simplify the left side.

Tap for more steps...

Step 1.1.3.2.1

Cancel the common factor of $12$ .

Tap for more steps...

Step 1.1.3.2.1.1

Cancel the common factor.

$\frac{12 \frac{d y}{d t}}{12} = \frac{- 9.6}{12}$

Step 1.1.3.2.1.2

Divide $\frac{d y}{d t}$ by $1$ .

$\frac{d y}{d t} = \frac{- 9.6}{12}$

Step 1.1.3.3

Simplify the right side.

Tap for more steps...

Step 1.1.3.3.1

Divide $- 9.6$ by $12$ .

$\frac{d y}{d t} = - 0.8$

Step 1.2

Rewrite the equation.

$d y = - 0.8 d t$

Step 2

Integrate both sides.

Tap for more steps...

Step 2.1

Set up an integral on each side.

$\int d y = \int - 0.8 d t$

Step 2.2

Apply the constant rule.

$y + C_{1} = \int - 0.8 d t$

Step 2.3

Apply the constant rule.

$y + C_{1} = - 0.8 t + C_{2}$

Step 2.4

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

$y = - 0.8 t + K$