Question

11>x ²y² x² dx 12yx² - cos y²dy = 0 ,

Answer 1

To solve the given equation, integrate the terms separately with respect to x and y. Set the equation equal to zero and simplify to find the solution.

Step-by-step explanation:

The given equation is:

11 > x²y²x² dx + 12yx² - cos y² dy = 0

To solve this equation, we need to integrate the terms with respect to x and y separately.

Integrating the term with respect to x, we get:

∫(11x²y²x²)dx = 11 ∫x²y²)dx = 11 /3 x³y² + C

Integrating the term with respect to y, we get:

∫(12yx² - cos y²)dy = 6yx²y - sin y² + C

Setting the equation equal to 0, we have:

11 /3 x³y² + 6yx²y - sin y² + C = 0

Therefore, the solution to the equation is:

11 /3 x³y² + 6yx²y - sin y² = -C