y=c1e^(at)cos(bt) +c2e^(at)sin(bt), where r = a+bi solve linear system of DEs from matrix form repeated roots how to convert linear system of DEs to matrix form GS for 2nd order DE complex roots find GS of 2nd order DE

GS for 2nd order DE complex roots

y=c1e^(rt)+c2te^(rt)+c3t^2e^(rt) + (...) find GS of 2nd order DE solve linear system of DEs from matrix form repeated roots solve linear system of DEs from matrix form complex roots GS for 2nd order DE repeated roots

GS for 2nd order DE repeated roots

X' = AX + F GS for 2nd order DE complex roots GS for 2nd order DE real roots how to convert linear system of DEs to matrix form find GS of homogeneous linear system

how to convert linear system of DEs to matrix form

X = c1V1e(lambda1t) + c2V2e(lambda2t) solving nonhomogeneous 2nd order DE GS for 2nd order DE repeated roots GS for 2nd order DE complex roots solve linear system of DEs from matrix form real roots

solve linear system of DEs from matrix form real roots

X = c1e^at(B1cos(bt)-B2sin(bt)) + c2e^at(B2cos(bt)+B1sin(bt)) solve linear system of DEs from matrix form complex roots find GS of 2nd order DE solving nonhomogeneous 2nd order DE find GS of homogeneous linear system

solve linear system of DEs from matrix form complex roots

x = c1V1e^lambdat)+c3(V2te^lambda2t+pe^lambda2t), (A-lambdaI)p = V solve linear system of DEs from matrix form repeated roots solve linear system of DEs from matrix form complex roots find GS of 2nd order DE solving nonhomogeneous 2nd order DE

solve linear system of DEs from matrix form repeated roots

1. convert to matrix form (X' = AX) 2. find eigenvalue (det(A-lambdaI) = 0 3. find eigenvectors for each lambda (augment A -lambda I and row reduce) 4. sub into general form for type of system GS for 2nd order DE repeated roots solving nonhomogeneous 2nd order DE GS for 2nd order DE complex roots find GS of homogeneous linear system

find GS of homogeneous linear system

Final Review Math 244

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Calculus - Geometry

user_kumartyv Created by 6 mon ago

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1. write char equation 2. solve for roots 3. substitute each root into general form

y = c1e^(rt)+c2e^(rt)

y=c1e^(at)cos(bt) +c2e^(at)sin(bt), where r = a+bi

y=c1e^(rt)+c2te^(rt)+c3t^2e^(rt) + (...)

X' = AX + F

X = c1V1e(lambda1t) + c2V2e(lambda2t)

X = c1e^at(B1cos(bt)-B2sin(bt)) + c2e^at(B2cos(bt)+B1sin(bt))

x = c1V1e^lambdat)+c3(V2te^lambda2t+pe^lambda2t), (A-lambdaI)p = V

1. convert to matrix form (X' = AX) 2. find eigenvalue (det(A-lambdaI) = 0 3. find eigenvectors for each lambda (augment A -lambda I and row reduce) 4. sub into general form for type of system

find complementary solution by setting DE to 0. then guess Yp to be of the same form that RHS is. Take the derivative of this Yp guess twice, then sub it into OG DE, solve for A. multiply guess by x for each term that matches complementary solution if present.

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Final Review Math 244

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