Which of the following is the general solution of the differential equation dy dx equals the quotient of 8 times x and y

Question

options -

a) y² = x² + C

b)x² - y² = C

c)y² = 4x² + C

d)y² = 8x² + C

I think its D

Answer 1

dy / dx = 8x / y

y dy = 8x dx

∫y dy = 8 ∫x dx

y²/2 = 8x²/2 + C₁

 y² = 8x² + 2C₁

 

2C₁= C

Therefore:

 y² = 8x² + C

Yes, it is D. I also tried y / 8x but the answer is not among the choices.

Answer 2

I agree

dy/dx = 8x/y

y dy = 8x dx

(1/2)y^2 = 4x^2 + c

y^2 = 8x^2 + 2c