The bottom two questions are wrong (A&D). A can't be 10, that is wrong. D can't be -4, that is wrong as well. Step 4We have found the following particular solution and its derivatives.Yp = Ax² + Bx + C + (Dx + E)e*= 2AX + B + (Dx + E)ex + Dex= 2A + (Dx + E)ex + 2De*Substituting into the original differential equation results in the following.y" - 8y' + 20y = 200x² - 52xe*ур4YP(2A + (Dx + E)e* + 2Dex) - 8(2Ax + B + (Dx + E)ex + Dex) + 20(Ax² + Bx + C + (Dx + E)ex) = 200x² - 52xe*Simplifying the left side of this equation gives the following.5(2A+ (Dx + E)ex + 2De*) - 8(2Ax + B + (Dx + E)ex + Dex)+ 20(Ax² + Bx + C + (Dx + E)e*)= (2A – 8B + 20C) + (−16A + 20B)x + (−6D + 13E)e* +(13✓ )oxe* + (20JAx²As the coefficients of the terms in this simplified expression must be equal to the coefficients of 200x² - 52xe, we have the following system.2A - 8B + 20C = 0-16A + 20B = 0-6D + 13E = 0) D =* A = 200ILX-52

Answered: Image /qna-images/answer/114b965f-a96b-4a14-911e-3741e149006c.jpg

We have found the following particular solution and its derivatives. Yp = Ax² + Bx + C + (Dx + E)e* Yp = 2AX + B + (Dx + E)e* + Dex = 2A + (Dx + E)e* + 2De* "1 Ур Substituting into the original differential equation results in the following. y" - 8y' + 20y = 200x² - 52xe* (2A + (Dx + E)e* + 2Dex) - 8(2Ax + B+ (Dx + E)ex + Dex) + 20(Ax2 + Bx + C+ (Dx + E)ex) = 200x² - 52xe*' Simplifying the left side of this equation gives the following. (2A+ (Dx + E)ex + 2Dex) - 8(2Ax+ B + (Dx + E)ex + De*) + 20(Ax² + Bx + C + (Dx + E)e*) = (2A - 8B + 20C) + (-16A + 20B)x+ (-6D+ 13E)e* + ²+( 13 ✓ )oxe* + (20 4x² As the coefficients of the terms in this simplified expression must be equal to the coefficients of 200x² - 52xe, we have the following system. 2A8B+20C = 0 -16A + 20B = -6D + 13E=0 x )D x 4 = 200 = -52

We have found the following particular solution and its derivatives. Yp = Ax² + Bx + C + (Dx + E)e* Yp = 2AX + B + (Dx + E)e* + Dex = 2A + (Dx + E)e* + 2De* "1 Ур Substituting into the original differential equation results in the following. y" - 8y' + 20y = 200x² - 52xe* (2A + (Dx + E)e* + 2Dex) - 8(2Ax + B+ (Dx + E)ex + Dex) + 20(Ax2 + Bx + C+ (Dx + E)ex) = 200x² - 52xe' Simplifying the left side of this equation gives the following. (2A+ (Dx + E)ex + 2Dex) - 8(2Ax+ B + (Dx + E)ex + De) + 20(Ax² + Bx + C + (Dx + E)e) = (2A - 8B + 20C) + (-16A + 20B)x+ (-6D+ 13E)e + ²+( 13 ✓ )oxe* + (20 4x² As the coefficients of the terms in this simplified expression must be equal to the coefficients of 200x² - 52xe, we have the following system. 2A8B+20C = 0 -16A + 20B = -6D + 13E=0 x )D x 4 = 200 = -52

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.1: Solutions Of Elementary And Separable Differential Equations

Problem 59E: According to the solution in Exercise 58 of the differential equation for Newtons law of cooling,...

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