Laplace transform help please: L{y′(t)}(s)=∫∞0e−sty′(t)dt

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drivera001

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Laplace transform help please: L{y′(t)}(s)=∫∞0e−sty′(t)dt

[FONT=&quot](1 point) Find the formula for the Laplace transform of the derivative of a function [/FONT][FONT=&quot][/FONT][FONT=&quot][FONT=MathJax_Math-italic]y[/FONT][FONT=MathJax_Main]′[/FONT]y′[/FONT][FONT=&quot]. Use the initial condition [/FONT][FONT=&quot][/FONT][FONT=&quot][FONT=MathJax_Math-italic]y[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]0[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Math-italic]y[/FONT][FONT=MathJax_Main]0[/FONT]y(0)=y0[/FONT][FONT=&quot], use [/FONT][FONT=&quot][/FONT][FONT=&quot][FONT=MathJax_Math-italic]y[/FONT]y[/FONT][FONT=&quot] and [/FONT][FONT=&quot][/FONT][FONT=&quot][FONT=MathJax_Math-italic]y[/FONT][FONT=MathJax_Main]′[/FONT]y′[/FONT][FONT=&quot]respectively for [/FONT][FONT=&quot][/FONT][FONT=&quot][FONT=MathJax_Math-italic]y[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math-italic]t[/FONT][FONT=MathJax_Main])[/FONT]y(t)[/FONT][FONT=&quot] and [/FONT][FONT=&quot][/FONT][FONT=&quot][FONT=MathJax_Math-italic]y[/FONT][FONT=MathJax_Main]′[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math-italic]t[/FONT][FONT=MathJax_Main])[/FONT]y′(t)[/FONT][FONT=&quot] and [/FONT][FONT=&quot][/FONT][FONT=&quot][FONT=MathJax_Math-italic]Y[/FONT]Y[/FONT][FONT=&quot] for the Laplace transform of [/FONT][FONT=&quot][/FONT][FONT=&quot][FONT=MathJax_Math-italic]y[/FONT]y[/FONT][FONT=&quot]. [/FONT]
[FONT=&quot][/FONT][FONT=MathJax_Math-italic]L[/FONT][FONT=MathJax_Main]{[/FONT][FONT=MathJax_Math-italic]y[/FONT][FONT=MathJax_Main]′[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math-italic]t[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]}[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math-italic]s[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Size2]∫[/FONT][FONT=MathJax_Main]∞[/FONT][FONT=MathJax_Main]0[/FONT][FONT=MathJax_Math-italic]e[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Math-italic]s[/FONT][FONT=MathJax_Math-italic]t[/FONT][FONT=MathJax_Math-italic]y[/FONT][FONT=MathJax_Main]′[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math-italic]t[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Math-italic]d[/FONT][FONT=MathJax_Math-italic]t[/FONT]L{y′(t)}(s)=∫0∞e−sty′(t)dt[FONT=&quot] [/FONT]

[FONT=&quot][/FONT][FONT=MathJax_Math-italic]u[/FONT][FONT=MathJax_Main]=[/FONT]u=[FONT=&quot] [/FONT][FONT=&quot] [/FONT][FONT=&quot][/FONT][FONT=&quot][/FONT][FONT=&quot][FONT=MathJax_Math-italic]d[/FONT][FONT=MathJax_Math-italic]v[/FONT][FONT=MathJax_Main]=[/FONT]dv=[/FONT][FONT=&quot] [/FONT][FONT=&quot][/FONT]

[FONT=&quot][/FONT][FONT=MathJax_Math-italic]d[/FONT][FONT=MathJax_Math-italic]u[/FONT][FONT=MathJax_Main]=[/FONT]du=[FONT=&quot] [/FONT][FONT=&quot] [/FONT][FONT=&quot][/FONT][FONT=&quot][/FONT][FONT=&quot][FONT=MathJax_Math-italic]v[/FONT][FONT=MathJax_Main]=[/FONT]v=[/FONT][FONT=&quot] [/FONT][FONT=&quot] [/FONT][FONT=&quot][/FONT]

[FONT=&quot][/FONT][FONT=MathJax_Main]=[/FONT]=[FONT=&quot] [/FONT][FONT=&quot][/FONT][FONT=&quot][/FONT][FONT=MathJax_Main]∣[/FONT][FONT=MathJax_Main]∣[/FONT][FONT=MathJax_Main]∣[/FONT][FONT=MathJax_Main]∞[/FONT][FONT=MathJax_Main]0[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Size2]∫[/FONT][FONT=MathJax_Main]∞[/FONT][FONT=MathJax_Main]0[/FONT]|0∞+∫0∞[FONT=&quot] [/FONT][FONT=&quot][/FONT]

[FONT=&quot][/FONT][FONT=MathJax_Main]=[/FONT]=




Need help with the last part. Thanks in advance
 
drivera001 said:
(1 point) Find the formula for the Laplace transform of the derivative of a function [FONT=MathJax_Math-italic]y[FONT=MathJax_Main]′[/FONT]y′[/FONT]. Use the initial condition [FONT=MathJax_Math-italic]y[FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]0[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Math-italic]y[/FONT][FONT=MathJax_Main]0[/FONT]y(0)=y0[/FONT], use [FONT=MathJax_Math-italic]yy[/FONT] and [FONT=MathJax_Math-italic]y[FONT=MathJax_Main]′[/FONT]y′[/FONT]respectively for [FONT=MathJax_Math-italic]y[FONT=MathJax_Main]([/FONT][FONT=MathJax_Math-italic]t[/FONT][FONT=MathJax_Main])[/FONT]y(t)[/FONT] and [FONT=MathJax_Math-italic]y[FONT=MathJax_Main]′[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math-italic]t[/FONT][FONT=MathJax_Main])[/FONT]y′(t)[/FONT] and [FONT=MathJax_Math-italic]YY[/FONT] for the Laplace transform of [FONT=MathJax_Math-italic]yy[/FONT].
[FONT=MathJax_Math-italic]L[/FONT][FONT=MathJax_Main]{[/FONT][FONT=MathJax_Math-italic]y[/FONT][FONT=MathJax_Main]′[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math-italic]t[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]}[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math-italic]s[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Size2]∫[/FONT][FONT=MathJax_Main]∞[/FONT][FONT=MathJax_Main]0[/FONT][FONT=MathJax_Math-italic]e[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Math-italic]s[/FONT][FONT=MathJax_Math-italic]t[/FONT][FONT=MathJax_Math-italic]y[/FONT][FONT=MathJax_Main]′[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math-italic]t[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Math-italic]d[/FONT][FONT=MathJax_Math-italic]t[/FONT]L{y′(t)}(s)=∫0∞e−sty′(t)dt

[FONT=MathJax_Math-italic]u[/FONT][FONT=MathJax_Main]=[/FONT]u=[FONT=MathJax_Math-italic]d[FONT=MathJax_Math-italic]v[/FONT][FONT=MathJax_Main]=[/FONT]dv=[/FONT]

[FONT=MathJax_Math-italic]d[/FONT][FONT=MathJax_Math-italic]u[/FONT][FONT=MathJax_Main]=[/FONT]du=[FONT=MathJax_Math-italic]v[FONT=MathJax_Main]=[/FONT]v=[/FONT]

[FONT=MathJax_Main]=[/FONT]=[FONT=MathJax_Main]∣[/FONT][FONT=MathJax_Main]∣[/FONT][FONT=MathJax_Main]∣[/FONT][FONT=MathJax_Main]∞[/FONT][FONT=MathJax_Main]0[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Size2]∫[/FONT][FONT=MathJax_Main]∞[/FONT][FONT=MathJax_Main]0[/FONT]|0∞+∫0∞

[FONT=MathJax_Main]=[/FONT]=

Need help with the last part.
Click to expand...
For some reason, all of your mathematical characters are repeated. I suspect that a copy-n-paste went awry. Were you not able to see your message after posting?

I think you meant to post the following:


Find the formula for the Laplace transform of the derivative of a function y′. Use the initial condition y(0) = y0, use y and y′ respectively for y(t) and y′(t) and Y for the Laplace transform of y.

. . . . .\(\displaystyle L\{y'(t)\}(s)\, =\, \int_0^{\infty}\, e^{-st}\, y'(t)\, dt\)


Is the above correct?

I couldn't understand the rest of what you posted. Kindly please reply with a clear statement of the remainder of the exercise statement, along with a listing of your steps so far, which have led you to "the last part" where you're getting stuck.

Please be complete. Thank you! ;)
 
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