Question

Consider the differential equation dy/dx = x^4(y - 2). Find the particular solution y = f(x) to the given differential equation with the initial condition f(0) = 0.

Is this y=e^(x^5/5)+4?

Answer 1

dy/(y-2) = x^4 dx
ln(y-2) = x^5/5 + ln(c)
y-2 = c e^(x^5/5)
y(0)=0, so c=-2.

y = 2-2e^(1/5 x^5)

I suspect you did

ln(y-2) = x^5/5 + c
y-2 = e^(x^5/5) + c
That still does not give your answer. Too bad you didn't show your work ...