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The solution at (x, t) = (2, 1) of the partial differential equation, 
subject to initial condition of u(x, 0) = 5x and 
subject to initial condition of u(x, 0) = 5x and - a)7
- b)11
- c)21
- d)31
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The solution at (x, t) = (2, 1) of the partial differential equation,s...
Concept:
where -∞ < x < ∞ , t > 0 and c > 0.
Satisfying the conditions u(x, 0) = f(x) and
where f(x) = initial displacement and g(x) is the initial velocity.
The solution for the above equation satisfying the conditions is given by D-Alembert's formula i.e.
Calculation:
Given:
Initial condition u(x, 0) = 5x ⇒ f(x) and
∴ the D-Alembert solution is
Putting the values of x = 2, t = 1, c = 6 and g(x) = 1
f(x) = 5x
f(- 4) = -20 and f(8) = 40 and
u(2, 1) = 10 + 1 ⇒ 11
where -∞ < x < ∞ , t > 0 and c > 0.Satisfying the conditions u(x, 0) = f(x) and
where f(x) = initial displacement and g(x) is the initial velocity.The solution for the above equation satisfying the conditions is given by D-Alembert's formula i.e.
Calculation:
Given:
Initial condition u(x, 0) = 5x ⇒ f(x) and
∴ the D-Alembert solution is
Putting the values of x = 2, t = 1, c = 6 and g(x) = 1
f(x) = 5x
f(- 4) = -20 and f(8) = 40 and
u(2, 1) = 10 + 1 ⇒ 11
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The solution at (x, t) = (2, 1) of the partial differential equation,subject to initial condition of u(x, 0) = 5x anda)7b)11c)21d)31Correct answer is option 'B'. Can you explain this answer?
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