anonymous
  • anonymous
solve the initial value problem du/dt = (t+1)/sqrt(t); u(1) = 4
Mathematics
schrodinger
  • schrodinger
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amistre64
  • amistre64
\[\int\limits_{} \frac{t+1}{\sqrt{t}} dt\]
amistre64
  • amistre64
split the fraction in two and work each side
amistre64
  • amistre64
{S} t.(t^-1/2) + t^(-1/2) dt {S} t^(1/2) + t^(-1/2) dt

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amistre64
  • amistre64
t^(3/2) t^(1/2) ----- + ------ + C 3/2 1/2
amistre64
  • amistre64
when t = 1; this should equal 4 according to the initial condition
amistre64
  • amistre64
2/3 + 2 +C = 4 8/3 +C = 4 C = 4 - 8/3 = -16/3 if i did it right
amistre64
  • amistre64
\[\frac{2t^2}{3}+\frac{2\sqrt{t}}{1}-\frac{16}{3}\]
anonymous
  • 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.
anonymous
  • anonymous
though solving for c = 4/3, but otherwise it's golden
amistre64
  • amistre64
:) youre welcome
amistre64
  • amistre64
yeah, the integrating i can do.... addition? nah lol
anonymous
  • anonymous
haha it's cool. i'm usually the same way- just apparently brain dead tonight

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