Calculus Examples

$1 (2 - 1) d x + (1 + 1) d y = 0$

Step 1

Subtract $1 (2 - 1) d x$ from both sides of the equation.

$(1 + 1) d y = - 1 (2 - 1) d x$

Step 2

Integrate both sides.

Tap for more steps...

Step 2.1

Set up an integral on each side.

$\int 1 + 1 d y = \int - (2 - 1) d x$

Step 2.2

Integrate the left side.

Tap for more steps...

Step 2.2.1

Add $1$ and $1$ .

$\int 2 d y = \int - (2 - 1) d x$

Step 2.2.2

Apply the constant rule.

$2 y + C_{1} = \int - (2 - 1) d x$

Step 2.3

Integrate the right side.

Tap for more steps...

Step 2.3.1

Simplify.

Tap for more steps...

Step 2.3.1.1

Subtract $1$ from $2$ .

$2 y + C_{1} = \int - 1 \cdot 1 d x$

Step 2.3.1.2

Multiply $- 1$ by $1$ .

$2 y + C_{1} = \int - 1 d x$

Step 2.3.2

Apply the constant rule.

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

Step 2.4

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

$2 y = - x + K$

Step 3

Divide each term in $2 y = - x + K$ by $2$ and simplify.

Tap for more steps...

Step 3.1

Divide each term in $2 y = - x + K$ by $2$ .

$\frac{2 y}{2} = \frac{- x}{2} + \frac{K}{2}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{- x}{2} + \frac{K}{2}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- x}{2} + \frac{K}{2}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Move the negative in front of the fraction.

$y = - \frac{x}{2} + \frac{K}{2}$

Step 4

Simplify the constant of integration.

$y = - \frac{x}{2} + K$