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1-) let fCE) be a differentiasle funckion. Show that pCe) dwce) = cA)wC6) - ecalwca) 3) Solue the following stoche stic differential equation: dx CE) = B xCE) + adwCt) xC0) = Then use t he resulle of the previous exercise () to show thats -p Ct-s) XCE) = Xoe + Lw CE). %3D

1-) let fCE) be a differentiasle funckion. Show that pCe) dwce) = cA)wC6) - ecalwca) 3) Solue the following stoche stic differential equation: dx CE) = B xCE) + adwCt) xC0) = Then use t he resulle of the previous exercise () to show thats -p Ct-s) XCE) = Xoe + Lw CE). %3D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1.) Let fCE) bea differentiasle function. Show that, %3D 9) Solue the folllouing stochestic differential equation: dx CE) = B xCE) + adw Ct) xCo) = Then use the resulle of the previous exercise () to show thats 7. -p Ct- s) XCE) = x,e' + duCE) -CawCL) WCE)e %3D
Transcribed Image Text:1.) Let fCE) bea differentiasle function. Show that, %3D 9) Solue the folllouing stochestic differential equation: dx CE) = B xCE) + adw Ct) xCo) = Then use the resulle of the previous exercise () to show thats 7. -p Ct- s) XCE) = x,e' + duCE) -CawCL) WCE)e %3D
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4. Consider the following function: I – 2, -2 < I < -1 -1< r<1 f(2) = %3D 2 – 1, 1<r<2. (i) Sketch the graph of f and find its Fourier series on [-2, 2). (ii) Use the obtained series to deduce that: 1 and 2k – 1)“ (2k 1)2 8 96
Transcribed Image Text:4. Consider the following function: I – 2, -2 < I < -1 -1< r<1 f(2) = %3D 2 – 1, 1<r<2. (i) Sketch the graph of f and find its Fourier series on [-2, 2). (ii) Use the obtained series to deduce that: 1 and 2k – 1)“ (2k 1)2 8 96
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