Question

Let y=f(x) be the particular solution to the differential equation dy/dx=2x−1/y^2 with the initial condition y(0)=3. Which of the following is an expression for f(x)?
A. √(x^2−x+9)

B. −3/3x^2−3x−1

C. (3x^2−3x)^1/3+3

D. (3x^2−3x+27)^1/3

Answer 1

Answer:

its D, i did it for an exam

Answer 2

Answer:

D. (3x^2-3x+27)^1/3

Step-by-step explanation:

dy/dx=2x−1/y^2

Cross multiply to get Y's and X's on different sides.

(y^2)dy = (2x-1)dx

Take the integral of each side

∫(y^2)dy = ∫(2x-1)dx

y^3/3 = 2x^2/2 - x + C

Multiply both sides by 3

y^3 = 3x^2 - 3x + C

Plug in (0,3) and solve for C

27 = 0 - 0 + C

C = 27

Plug in C to the equation

y^3 = 3x^2-3x+27

Cube root both sides to get just y

y = √(3x^2-3x+27)

y = (3x^2-3x+27)^1/3

D.