Calculus Examples

$x^{2} y - x^{2} + 4 y = 0$

Step 1

Add $x^{2}$ to both sides of the equation.

$x^{2} y + 4 y = x^{2}$

Step 2

Factor $y$ out of $x^{2} y + 4 y$ .

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Step 2.1

Factor $y$ out of $x^{2} y$ .

$y x^{2} + 4 y = x^{2}$

Step 2.2

Factor $y$ out of $4 y$ .

$y x^{2} + y \cdot 4 = x^{2}$

Step 2.3

Factor $y$ out of $y x^{2} + y \cdot 4$ .

$y (x^{2} + 4) = x^{2}$

Step 3

Divide each term in $y (x^{2} + 4) = x^{2}$ by $x^{2} + 4$ and simplify.

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Step 3.1

Divide each term in $y (x^{2} + 4) = x^{2}$ by $x^{2} + 4$ .

$\frac{y (x^{2} + 4)}{x^{2} + 4} = \frac{x^{2}}{x^{2} + 4}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $x^{2} + 4$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{y (x^{2} + 4)}{x^{2} + 4} = \frac{x^{2}}{x^{2} + 4}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{x^{2}}{x^{2} + 4}$