Here's the question you clicked on:
emma29
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.
think you're making it too hard...
\[(t+1)y' + y = ( (t+1)*y)'\]
sorry i'm just trying it out
am i suppose to end up with something like this?\[y dy=cost/(t+1) dt\] and then integrate both sides?
hmm you're mixing methods:) you have:
\[( (t+1)*y)' = \cos(t)\]
\[\int\limits_{ }^{ }( (t+1)*y)' = \int\limits_{ }^{ }\cos(t)\]
\[(t+1)*y= \sin(t) +C\] whoops
ok i'll try this out..thanks
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 :'(
oh wow i made a mistake when taking the integral of \[\int\limits1/(1+t) \] no wonder it wouldn't come out nicely..thanks
thanks to both for your help!!