Question

Let A and k be positive constants. Which of the given functions is a solution to dy/dt=k(y+A).I got y= A^-1 + Ce^Akt but I'm not sure.

Answer 1

Answer:

$y=-A+Ce^{kt}$

Step-by-step explanation:

Let A and k be positive constants

$\frac{dy}{dt} =k(y+A)$

Here k and A  are constant.

$\frac{dy}{dt} =k(y+A)$

multiply both sides by dt

$dy=k(y+A)dt$

$\frac{dy}{y+A} =kdt$

Integrate on both sides

$ln|y+A|=kt+C$

Now solve for y. convert it into exponential form

$y+A=e^{kt+C}$

$y+A=e^{kt}e^C$

$y+A=Ce^{kt}$

Subtract A from both sides

$y=-A+Ce^{kt}$