Question

**Calc 2 Help Needed** Solve the initial value problem below:

(t^2 + 2t)dx/dt = 2x + 5 with t, x>0 and x(1) = 1

Answer 1

Didn't i solved this

Answer 2

I needed additional assistance.. I understand to split and integrate, but don't know where to head afterwards?

Answer 3

Once you integrate you get
\[\ln{(2x+5)}=\frac{1}{2}\ln(\frac{t}{t+2})+c\]
put x=1 and t=1 to find c

Answer 4

\[c=\ln(7\sqrt3)\]

Answer 5

ok makes sense so far..

Answer 6

That is it nothing is unknown now

Answer 7

so how do I slove for x(t) now?

Answer 8

ln(7) - (ln(1/3))/2??

Answer 9

ahh that didn't work online.

Answer 10

are you still there??