The graph of a function f is shown. Use the differential equation and the given point to find an equation of the function. dy/dx=4x+(9x^2/(3x^3+1)^(3/2))

Question

and the point (0,2) using the substitution method of integration.

Answer 1

y' = 4x+(9x^2/(3x^3+1)^(3/2))
y = 2x^2 - 2/√(3x^3+1) + C
Now plug in (0,2) to find C.

integrate using u = 3x^3+1, so
du = 9x^2 dx