Find the solution to the differential equation dBdt6B30 with

Solution

Find the solution to the differential equation (dB/dt)+6B=30 with B(1)=70 (dB/dt)+6B=30 LINEAR DIFF. EQN. integration factor is i(t) = exp(\\int 6 dt) = exp(6t) = e^(6t) B(t) . i(t) = \\int 30 i(t) dt + C B(t) .e^(6t) = \\int 30 e^(6t) dt + C B(t) .e^(6t) = 30 ( e^(6t) ) / 6 + C B(t) .e^(6t) = 5 e^(6t) + C B(t) = 5 + C . exp(-6t) B(1)=70 ==> 70 = 5+ C exp(-1) C e^(-1) = 65 C/e = 65 C= 65 e B(t) = 5 + C . exp(-6t) B(t) = 5 + 65 . e^(-6t) . e B(t) = 5 + 65 . e^(1-6t) ANSWER