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Veryfing ODE for complicated y(t) 
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#1
Jan2812, 01:48 PM

P: 11

1. The problem statement, all variables and given/known data
For the differential equation, verify (by differentiation and substitution) that the given function y(t) is a solution. 2. Relevant equations [itex] y'  4ty = 1 [/itex] [itex] y(t) = \int_{0}^{t} e^{2(s^{2}t^{2})} ds[/itex] 3. The attempt at a solution I attempted to take [itex]\frac{d}{dt}[/itex] of y(t) as usual but 1. if I do not try bringing the [itex]\frac{d}{dt}[/itex] inside the integral I can do nothing because there is no elementary antiderivative of y(t). 2. if I do bring the [itex]\frac{d}{dt}[/itex] inside the integral, I can use the chain rule to get [itex] y(t) = (2) \int_{0}^{t} (2t) e^{2(s^{2}t^{2})} ds[/itex] but since my variable of integration is ds not dt, this doesn't allow me to use a usubstitution as I had hoped nor can I think of a way to relate ds and dt. More or less I do not know how to take [itex]\frac{d}{dt}[/itex] of y(t) and I do not know any other ways to solve the problem. 


#2
Jan2812, 02:23 PM

P: 43

Do you have to do it that way? Because it looks like you can solve it linearly.



#3
Jan2812, 02:56 PM

P: 11

Yes, the problem asks to verify that y(t) is a solution to the differential equation y' + 4ty = 1.



#4
Jan2812, 04:34 PM

Sci Advisor
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Thanks
P: 25,228

Veryfing ODE for complicated y(t)



#5
Jan2812, 09:30 PM

P: 11

Thanks! 


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