341test1key - M ath 341 Section O il: Test #1 This test,...

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Unformatted text preview: M ath 341 Section O il: Test #1 This test, has 6 questions on 6 pages. Each question is worth the same. 1. Find the g eneral solution of the differential equation w J 1 = — -3*" + C <-3X - ,, (1) L +C 3^- C v . „ \T 2. Solve t he i nitial value problem = 5. - =£ 2. / ,^ z — ry _ i— 3 3-x ^ *^3 T ^ / I w -X u = *X / /-. + C. = 32 - 2. , 8 OC T- - -x 3. Solve the initial value problem dx at 2 = J, —J, , T T - 2. y. (i - ^L u -x -f- 'X f =» // f c X 0- 4. Consider the d ifferential equation x-'V + 2xV - Gy = 0. (1) 4a. Verify t hat each of the f unctions y\ x2 and y<2 = :c~'! is a solution of the e quation. = ^ =? " - X' 3 4b. Solve tlu; initial value problem consisting of the equation (1) together with the i nitial conditions y(2) = 10 and y'(1) = 15. -3B B 8~ 38 , 15 16 ^ nfr i J2B J-b ~^} _— LL P( = 10 T <Si> 1*0 5= -3 5. Find the general solution of the differential equation f for — T I in — O '• r 9. =0 2. , 2 , -2 , - 2L e ce 2-X K£ -^ c 2 xe 2X -2* e -f CB z + t> 6. Consider t he nonhomogeneous differential e quation y" - 7y'+ 12y = Se2*. 6a. Find the "'complementary f unction" (in other words, the general solution to the corresponding homogeneous equation). r z -7r ^ 3-x 6b. Now let's look for a p articular solution. Let's try y = Ae2::'. Can you find a constant A t hat works? - (\^ ^ u'^At2* ^ 2f\1 = *„,":= >'"-2* u ...
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This note was uploaded on 12/07/2011 for the course MATH 341 taught by Professor Zhang during the Fall '08 term at University of Delaware.

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341test1key - M ath 341 Section O il: Test #1 This test,...

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