anonymous
  • anonymous
given (1+t)y' +y= cos(t) , y(0)=1 , I tried solving it using P(x) and q(x). So far I have d/dt(yt) = integral (cost/(1+t))*t dt...I'm stuck with the right side.
Differential Equations
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
think you're making it too hard...
anonymous
  • anonymous
\[(t+1)y' + y = ( (t+1)*y)'\]
anonymous
  • anonymous
make sense?

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anonymous
  • anonymous
hello?
anonymous
  • anonymous
sorry i'm just trying it out
anonymous
  • anonymous
k :)
anonymous
  • anonymous
am i suppose to end up with something like this?\[y dy=cost/(t+1) dt\] and then integrate both sides?
anonymous
  • anonymous
hmm you're mixing methods:) you have:
anonymous
  • anonymous
\[( (t+1)*y)' = \cos(t)\]
anonymous
  • anonymous
\[\int\limits_{ }^{ }( (t+1)*y)' = \int\limits_{ }^{ }\cos(t)\]
anonymous
  • anonymous
\[(t+1)*y= \sin(t) +C\] whoops
anonymous
  • anonymous
ok i'll try this out..thanks
Callisto
  • Callisto
I'm too stupid to solve in this way... \[(1+t)y' +y= cos(t)\]\[y' +\frac{1}{1+t}y= \frac{1}{1+t}cos(t)\] Nice :) \[\alpha = e^{\int\frac{1}{1+t}dt}=e^{\ln|1+t|} = 1+t\]\[y=\frac{1}{\alpha}\int \alpha \times \frac{1}{1+t}cos(t) dt = \frac{1}{1+t}\int (1+t) \times \frac{1}{1+t}cos(t) dt \]\[= \frac{1}{1+t}\int cost dt =...\] Why can't I make my life easier :'(
anonymous
  • anonymous
oh wow i made a mistake when taking the integral of \[\int\limits1/(1+t) \] no wonder it wouldn't come out nicely..thanks
anonymous
  • anonymous
thanks to both for your help!!

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