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anonymous
 4 years ago
diff eq..determine the form of a particular solution for the given nonhomogeneous equation
y''+2y'=34t
anonymous
 4 years ago
diff eq..determine the form of a particular solution for the given nonhomogeneous equation y''+2y'=34t

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amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1yp = some educated guess yp=At + B ; if these are not already a linear solution to the homogenous part ...

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0for fundamental solution set, i have y1=1, y2=e^(2t) f(t)=34t polynomial method so yp=At+B...check to see if any matches the fund.set. it does so... yp=At^2+Bt find y'p and y''p and plug in. now solving for A and B is where i'm stuck

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1then lets work thru it so I can catch up :)

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1r^2+2r=0 r=0,2 right?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0at this point, it's just algebra which apparently, i'm very weak at

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1\[y=c_1e^{0x}+c_2e^{2x}+y_p\] \[y=c_1+c_2e^{2x}+y_p\]

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1yp = At + B ; but we already have a constant so we need to up the ante yp = At^2 + Bt ; and derive

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1yp = At^2 + Bt yp'= 2At + B yp''= 2A agreed?

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1yp''+2yp'=34t (2A) + 2(2At + B)=34t im going to do this in lowercase, just easier to type for me 2a +4at +2b = 3 4t (4a)t = 4t ; a=1 (2a+2b) = 3 2+2b = 3 ; b=5/2

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ah ok, i almost did that to solve for a but wasn't sure if it was correct, thank you

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1at^2 + bt = t^2+ 5/2 t\[\] \[y=c_1+c_2e^{2x}t^2+\frac 52 t \]
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