Calculus Examples

$d y - x d x = 0$

Step 1

Add $x d x$ to both sides of the equation.

$d y = x d x$

Step 2

Integrate both sides.

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Step 2.1

Set up an integral on each side.

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

Step 2.2

Apply the constant rule.

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

Step 2.3

By the Power Rule, the integral of $x$ with respect to $x$ is $\frac{1}{2} x^{2}$ .

$y + C_{1} = \frac{1}{2} x^{2} + C_{2}$

Step 2.4

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

$y = \frac{1}{2} x^{2} + K$