Calculus Examples

$(y - x - 10) \frac{d y}{d x} = x - x$

Step 1

Separate the variables.

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Step 1.1

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

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Step 1.1.1

Subtract $x$ from $x$ .

$(y - x - 10) \frac{d y}{d x} = 0$

Step 1.1.2

Divide each term in $(y - x - 10) \frac{d y}{d x} = 0$ by $y - x - 10$ and simplify.

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Step 1.1.2.1

Divide each term in $(y - x - 10) \frac{d y}{d x} = 0$ by $y - x - 10$ .

$\frac{(y - x - 10) \frac{d y}{d x}}{y - x - 10} = \frac{0}{y - x - 10}$

Step 1.1.2.2

Simplify the left side.

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Step 1.1.2.2.1

Cancel the common factor of $y - x - 10$ .

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Step 1.1.2.2.1.1

Cancel the common factor.

$\frac{(y - x - 10) \frac{d y}{d x}}{y - x - 10} = \frac{0}{y - x - 10}$

Step 1.1.2.2.1.2

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

$\frac{d y}{d x} = \frac{0}{y - x - 10}$

Step 1.1.2.3

Simplify the right side.

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Step 1.1.2.3.1

Divide $0$ by $y - x - 10$ .

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

Step 1.2

Rewrite the equation.

$d y = 0 d x$

Step 2

Integrate both sides.

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Step 2.1

Set up an integral on each side.

$\int d y = \int 0 d x$

Step 2.2

Apply the constant rule.

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

Step 2.3

Integrate the right side.

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Step 2.3.1

The integral of $0$ with respect to $x$ 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 $D$ .

$y = D$