Calculus Examples

$\frac{d y}{d x} = 4 \frac{d w}{d x}$

Step 1

Rewrite the equation.

$d y = 4 d y$

Step 2

Integrate both sides.

Tap for more steps...

Step 2.1

Set up an integral on each side.

$\int d y = \int 4 d y$

Step 2.2

Apply the constant rule.

$y + C_{1} = \int 4 d y$

Step 2.3

Apply the constant rule.

$y + C_{1} = 4 y + C_{2}$

Step 2.4

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

$y = 4 y + K$

Step 3

Solve for $y$ .

Tap for more steps...

Step 3.1

Move all terms containing $y$ to the left side of the equation.

Tap for more steps...

Step 3.1.1

Subtract $4 y$ from both sides of the equation.

$y - 4 y = K$

Step 3.1.2

Subtract $4 y$ from $y$ .

$- 3 y = K$

Step 3.2

Divide each term in $- 3 y = K$ by $- 3$ and simplify.

Tap for more steps...

Step 3.2.1

Divide each term in $- 3 y = K$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{K}{- 3}$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $- 3$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{K}{- 3}$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{K}{- 3}$

Step 3.2.3

Simplify the right side.

Tap for more steps...

Step 3.2.3.1

Move the negative in front of the fraction.

$y = - \frac{K}{3}$

Step 4

Simplify the constant of integration.

$y = K$