## anonymous 5 years ago solve the initial value problem du/dt = (t+1)/sqrt(t); u(1) = 4

1. amistre64

$\int\limits_{} \frac{t+1}{\sqrt{t}} dt$

2. amistre64

split the fraction in two and work each side

3. amistre64

{S} t.(t^-1/2) + t^(-1/2) dt {S} t^(1/2) + t^(-1/2) dt

4. amistre64

t^(3/2) t^(1/2) ----- + ------ + C 3/2 1/2

5. amistre64

when t = 1; this should equal 4 according to the initial condition

6. amistre64

2/3 + 2 +C = 4 8/3 +C = 4 C = 4 - 8/3 = -16/3 if i did it right

7. amistre64

$\frac{2t^2}{3}+\frac{2\sqrt{t}}{1}-\frac{16}{3}$

8. anonymous

ahh thanks a ton. i was WAY overthinking it. used to other profs who constantly used all kinds of tricks and stuff so i was looking for something way more complicated. thanks again.

9. anonymous

though solving for c = 4/3, but otherwise it's golden

10. amistre64

:) youre welcome

11. amistre64

yeah, the integrating i can do.... addition? nah lol

12. anonymous

haha it's cool. i'm usually the same way- just apparently brain dead tonight