Question

We wish to solve the PDE utt = 25uxx, -? < x < ?, t > 0 Guess solutions of the form u = e?x+?t (find a relationship between ? and ?). Suppose you know u(x, 0) = ex. There are exactly two solutions of the above form, one with a positive ut(x, 0) and one with negative ut(x, 0). The first is: u = And the second is u =

          We wish to solve the PDE
utt = 25uxx, -? < x < ?, t > 0
Guess solutions of the form u = e?x+?t (find a relationship between ? and ?).
Suppose you know u(x, 0) = ex. There are exactly two solutions of the above form, one with a positive ut(x, 0) and one with negative ut(x, 0). The first is:
u =
And the second is
u =

We wish to solve the PDE
utt = 25uxx, -? < x < ?, t > 0
Guess solutions of the form u = e?x+?t (find a relationship between ? and ?).
Suppose you know u(x, 0) = ex. There are exactly two solutions of the above form, one with a positive ut(x, 0) and one with negative ut(x, 0). The first is:
u =
And the second is
u =

Added by Isabel M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

12/14/2022

Step 1

Substituting this into the PDE, we get: b * e^(ax + bt) = 25 * a^2 * e^(ax + bt) This simplifies to: b = 25 * a^2 This is the relationship between a and b. Now, we know that u(x,0) = e^x. This means that when t = 0, u = e^x. Show more…

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We wish to solve the PDE utt = 25uxx, -∞ < x < ∞, t > 0 Guess solutions of the form u = eᵃˣ⁺ᵇᵗ (find a relationship between α and β). Suppose you know u(x, 0) = eˣ. There are exactly two solutions of the above form, one with a positive uᵗ(x, 0) and one with negative uᵗ(x, 0). The first is: u = And the second is u = help (formulas)