Given the differential equation and its initial conditions y" + 8y' + 15y = 7x? - 10 with y(0) = 4 and y'(0) = - 10 The Specific Solution to its Particular Solution is 112 1564 3375 At this point our General Solution to the original differential equation is 112 1564 y(1) = C,e + C,e 15 225 3375 Find the values for C and C; by 1. Finding the first derivative of the general solution. 2. Plug the initial conditions into the general solution and the derivative of the general solution. 3. Use the resulting system of equations to find C, and C. 97 -7 125

Calculus: Early Transcendentals
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Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Given the differential equation and its initial conditions
y" + 8y' + 15y = 7x2 - 10 with y(0) = 4 and y'(0) = - 10
The Specific Solution to its Particular Solution is
7
112
1564
15
225
3375
At this point our General Solution to the original differential equation is
112
1564
y(1) = C,e
15
225
3375
Find the values for C and C, by
1. Finding the first derivative of the general solution.
2. Plug the initial conditions into the general solution and the derivative of the general solution.
3. Use the resulting system of equations to find C; and C.
97
27
A
-7
125
-71
19
B
-518
C =
147
86
-8
31
-43
27
312
C,=
125
173
27
(E)
C =
-243
125
17
31
C =
53
Transcribed Image Text:Given the differential equation and its initial conditions y" + 8y' + 15y = 7x2 - 10 with y(0) = 4 and y'(0) = - 10 The Specific Solution to its Particular Solution is 7 112 1564 15 225 3375 At this point our General Solution to the original differential equation is 112 1564 y(1) = C,e 15 225 3375 Find the values for C and C, by 1. Finding the first derivative of the general solution. 2. Plug the initial conditions into the general solution and the derivative of the general solution. 3. Use the resulting system of equations to find C; and C. 97 27 A -7 125 -71 19 B -518 C = 147 86 -8 31 -43 27 312 C,= 125 173 27 (E) C = -243 125 17 31 C = 53
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