Solving Separable Differential Equation with Initial Condition

[alchal]

QUESTION:

Solve the separable differential equation
dy/dx = sqrt(4y+64), Initial Condition: y(4)=9,
and find the particular solution satisfying the initial condition.

MY ATTEMPT:

(dy/dx)^2 = 4y+64
((dy/dx)^2)-4y = 64
,/' (((dy/dx)^2)-4y) dx = ,/' 64 dx

Is this the right method? If so, not sure how to integrate (dy/dx)^2

Any suggestions?

 

[JJacquelin]

dy/sqrt(4y+64) = dx

 

[alchal]

Thank you!