Question

Solve this differential equation
dT/dt = -3/25(T-25)

Answer 1

\[\frac{dT}{T-25}=-\frac{3}{25}dt\]integrate both sides\[\ln(T-25)=-\frac{3}{25}t\]\[\large{e^{\ln(T-25)}=e^{-\frac{3}{25}t}}\]

Answer 2

right lana :)

Answer 3

\[\large{T-25=e^{-\frac{3}{25}t}}\]

Answer 4

ah thank you ! :)

Answer 5

theres a +C after e^{3/2t}

Answer 6

forgot it -.- one min let me type the answer

Answer 7

\[\large{T=Ce^{-\frac{3}{25}t}+25}\]

Answer 8

just integrate both the sides

Answer 9

because when integrating\[\ln(T-25)=-\frac{3}{25}t+C\]so when u take e of both sides\[\large{e^{\ln(T-25)}=e^{-\frac{3}{25}t+C}}\]\[\large{\(T-25)=e^{-\frac{3}{2}t}e^c}\]e^c is just a constant so u can write it as C or any letter