Diff EquatLinear Algebra
Diff EquatLinear Algebra MTH 2201
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This 1 page Class Notes was uploaded by Mrs. Lenore King on Monday October 12, 2015. The Class Notes belongs to MTH 2201 at Florida Institute of Technology taught by Jay Kovats in Fall. Since its upload, it has received 50 views. For similar materials see /class/221670/mth-2201-florida-institute-of-technology in Mathematics (M) at Florida Institute of Technology.
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Date Created: 10/12/15
Math 2201 Final exam practice problems Some useful formulae You will not be given the rst two formulae on the exam so memorize them 0 If atbt are continuous on an interval I the general solution of the 1st order equation y aty bt on I is given y yt 67A eA bt dt Ce AO where At at and C is constant 0 If ftgt are piecewise continuous on 0 00 we de ne their convolution f 9f g by gt f f39rgt 7 7 d7quot For Fs Lft Cs Lgt we have the following results 0 1st Translation Theorem Le quotft Fs 7 a 0 2nd Translation Theorem Lft 7 aZt 7 a e 5Fs o Differentiation Theorem Lt ft 71 F s o Convolution Theorem gt F3Gs o DiracDelta Theorem L6t 7 a 6quot 1 Solve the initial value problem y 312g 12 z E R y1 1 2 a Solve the initial value problem zgy yz 7 l 0 z gt 0 y1 7r Hint the equation is separable b Solve the IV for the Bernoulli equation y y y 1 in R y0 2 c Is I 7 y dz I y dy 0 exact Are the coef cients homogeneous Find the general solution d Solve the IV y 2 7 xy 7 21 3 y0 73 e Solve y tan2 1 y f Solve 7ydz I mMy 0 3 Use your favorite method to nd a particular solution yp y Zy y 6 lnz 4 Solve the initialvalue problem for the CauchyEuler equation my 7 4y I4 on 000 yl 1 MG 5 Find a third order linear homogeneous differential equation that has 1 7 me as a solution 6 Use your favorite method to solve the initial value problem y y 12 y0 0 y 0 1 7 If one approaches the equation y 7 y e cosz 1 using the method of undetermined coef cients what will be the nal choice for the form of yp Do not solve just give your nal form of yp 8 Solve the initialvalue problem for the CauchyEuler equation 212y 51y y 0 on 0 00 y4 l y4 1 9 Find general solutions to the CauchyEuler equations on 0 00 12y 51y 3y 0 zgym zy 7 y 0 7x 71 1 2 1 10 Solve the initial value problem X lt 1 71 72gt X X0 lt2 0 0 5 3 oo 11 Let E anz be a solution to the equation y 7 I 1y 7 y 0 Find the recursive relationship of the n0 an and nd a2a3a4 in terms of a0 and a1 00 12 Find a solution of the form E anz to the equation y 7 my 0 n0 13 Find a solution of the form E anz to the equation I Dy 7 y 0 70 t if 0 lt t 2 14 Let ft T i lt 3t 7 2 If t 2 2 z 3 t tir t77 15 Use the convolutlon theorem to calculate L f0 s1n239r t 7 7 di L f0 7 6 dT L tfo 7 6 d39r l6 Solve the integral equations a at 7 7 f7 d r t b ta1 f Tft 7 7 d7quot 17 For gt t2 using only the de nition calculate the convolution gt Use the de nition of Laplace transform to calculate 18 Calculate 1W 45351 19 Use the Laplace transform to solve the following initial value problems a y y 6 7 90 07 M0 0 b y Mt 7 1 y0 a y 0 b c y 6t 7 1 y0 a yO b d y y 6G 7 W 37 90 07 W0 0