How to Derive the Decay Equation for Radioactive Isotopes A -> B -> C?

[unscientific]

Homework Statement

I learned that radio-decay is exponential; say if A decays to B with constant y₁ and B decays to C with constant y₂ and C is stable, N₁ is nuclei in A while N₂ is nuclei in B.

N₁ = N₀e^-y1(t)

Homework Equations

Then, I tried writing the decay equation for B, and hit a wall because N₂ is no longer N₀, as the amount originally is zero.

The Attempt at a Solution

Then i tried to derive it:
Amount = (decayed nuclei from A) + (decay of itself)

N₂ = INT A₁ dt + INT A₂ dt

and I arrive with this crazy integration which I do not know how to solve. Are there any better ways to derive it?

 

[epenguin]

This is the gentlest introduction to simultaneous or coupled differential equations, of which you will probably get a basinful later.

I think before anyone helps, you must actually write out the (three) equations you are trying to solve together.

But when you have done that you may see yourself how to go further and later lessons will not seem so out of the blue to you.