Seperation of Variables: t*(dy/dt) = 4*y, y(1) = 2, t > 0

[moy1989]

Hey guys can you tell me if I'm doing this right? Because supposedly it is a wrong answer. the problem is:

Use separation of variables to solve the IVP

t*(dy/dt) = 4*y, y(1) = 2, t > 0

So,

(1/t)*(dt/dy) = 1/(4*y)

(1/t)*(dt) = 1/(4*y)*(dy)

Integrate

ln(t) + c = (1/4)*ln(y)

solve for c

ln(1) + c = (1/4)*ln(2)

c = (1/4)*ln(2)

to solve for y(t)

4*ln(t) + 4*c = ln(y)

exp(4*ln(t)) + exp(c) = exp(ln(y))

t^4 + 2 = y(t)

 

[tkhunny]

Check your exponent rules.

\(\displaystyle e^{a+b} = e^{a} * e^{b} \ne e^{a} + e^{b}\)

 

[moy1989]

Thanks tkhunny