Calculus AB
posted by dyingincalc .
Verify if the given equations are solutions to the differential equation.
dy/dt=k(ya)
i) y=1ae^(kt)
ii) y=a+Ce^(kt)

dy/dt=k(ya) ... (1)
i) y=1ae^(kt) (particular solution)
differentiate y w.r.t. t:
d(1ae^(kt))/dt
= k(e^(kt)+a)ka
= kyka
= k(ya)
= righthand side, QED
ii) y=a+Ce^(kt)
differentiate with respect to t:
dy/dt
=Cke^(kt)
=k(a+Ce^(kt))ka
=kyka
=k(ya)
=righthand side QED