DIFFEQ exam 2- 4.3-6.3

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Calculus - Geometry

khalid1090phgs Created by 6 mon ago

Cards in this deck(33)

sec^2x

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-csc^2x

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secxtanx

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-cscxcotx

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xlnx - x + C

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-ln abs(secx) +1/2sec^2x+c

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v1'y1+v2'y2=0 v1'y1'+v2'y2'=f/a

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solve for v1 and v2 using elimination and integration

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yp(t)=v1y1+v2y2

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ln|secx+tanx|+C

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y1=e^atcos(Bt) y2=e^atsin(Bt)

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y1=e^r1t y2=e^r2t

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y1=te^r1t y2=e^r2t

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ar^2+(b-a)r+c=0, or at^2y''+bty'+cy=0

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y1=t^r1 y2=t^r3

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y1=t^r y2t^r(lnt)

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y1=t^a cos(Blnt) y2=t^a sin(Blnt)

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if you need a soln for t<0, replace with -t

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yp(t)=At+B

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yp(t)=Ae^t, yp(t)Ae^3t

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yp(t)=Asint+Bcost

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yp(t)=(at+b)e^tsint+(at+b)e^tcost, add in t if repeated root anywhere

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add together particular solutions

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1)put in d notation 2)cancel for one of the variables 3)solve with undetermined coefficients 4)plug x and y back into og equation to solve for coefficients or relate them

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w[f1,...,fn](x)=det(f1(x),,, f2(x),,,, fn(x): f'1(x).... :f''1(x)...:f^(n-1)1(x)...) find det normal way

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cos^2x-sin^2x

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2sinxcosx

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f1(x)=x, f2(x)=x^2, f3(x)=1-2x^2 c1x+c2x^2+c3(1-2x^2)=0, all coeff must equal 0 prove it

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(D-r)

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(D-r)^(k+1)

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(D^2+B^2)

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[(D-a)^2+B^2]^(k+1)

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leave out the homogeneous case in your answer, foil out annihilators that are confusing

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