nd integrate an exponential function. initial valued problem (IVP), find the solution

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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12:55 A
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1. (a) Critically outline with practical examples and illustrations of how to
Differentiate and integrate an exponential function.
(b)For the following initial valued problem (IVP), find the solution for
x> 0,Comment on your results.
3
y'" = 1+-+9Vx.
x2
x3
y(1) = 8
y'(1) = 9
y"(1) = 10
(c) Test for exactness and solve the IVP, critically outline the particular
solution
(x + 5e*y)dx = -e*dy
y(0) = -2
2(a) Given that f(x,y) = 6x²y³ – cosx + 5y – siny + 10x, establish
the fact that, the order in which the second order mixed partials
derivatives are taken ie immaterial
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Transcribed Image Text:12:55 A Done 1 1. (a) Critically outline with practical examples and illustrations of how to Differentiate and integrate an exponential function. (b)For the following initial valued problem (IVP), find the solution for x> 0,Comment on your results. 3 y'" = 1+-+9Vx. x2 x3 y(1) = 8 y'(1) = 9 y"(1) = 10 (c) Test for exactness and solve the IVP, critically outline the particular solution (x + 5e*y)dx = -e*dy y(0) = -2 2(a) Given that f(x,y) = 6x²y³ – cosx + 5y – siny + 10x, establish the fact that, the order in which the second order mixed partials derivatives are taken ie immaterial ADIemarke 1 Text editor Edit picture Fill Form Annotation
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