Wave Equation (Need Clarification Please)

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Challenege Q



I am supposed to take the Laplace transform of the wave equation that yields a non-homogeneous ordinary differential equation in terms of $mathcalLf(x)$ and $mathcalLu(x,t)$ and its $x$-derivatives.



Can someone please explain the relationship between the two function, and how it's $x$-derivatives changes will be reflected in the function. This question was posed as a challenge question, and I am seeking some guidance.




differential-equations pde partial-derivative wave-equation initial-value-problems




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  • Here's a MathJax tutorial :)
    – Shaun
    19 hours ago










  • I'm not sure what your question is. Applying the Laplace transform $$mathcalLg(boldsymbolx, t) = int_0^infty g(boldsymbolx, t) e^-st dt = tildeg(boldsymbolx, s)$$ to your problem yields $$s^2 tildeu - tildeu_xx = tildef$$ You'll need to convert your boundary conditions as well and then solve the above ODE.
    – Mattos
    18 hours ago











  • The boundary conditions are just simply between 0 and 1 as opposed to infinity? I don't understand how your response is yielding a equation in terms of Lf(x) and Lu(x,t). I'm quite lost how to transform on these nonspecific functions.
    – FireMeUP
    18 hours ago










  • Mattos, where did you get g(x,t)?
    – FireMeUP
    15 hours ago










  • Can you explain where you difficulty is? Do you know what the Laplace transform is, and have you tried applying it?
    – Strants
    15 hours ago














up vote
-1
down vote

favorite
3












Challenege Q



I am supposed to take the Laplace transform of the wave equation that yields a non-homogeneous ordinary differential equation in terms of $mathcalLf(x)$ and $mathcalLu(x,t)$ and its $x$-derivatives.



Can someone please explain the relationship between the two function, and how it's $x$-derivatives changes will be reflected in the function. This question was posed as a challenge question, and I am seeking some guidance.




differential-equations pde partial-derivative wave-equation initial-value-problems




share|cite|improve this question





















  • Here's a MathJax tutorial :)
    – Shaun
    19 hours ago










  • I'm not sure what your question is. Applying the Laplace transform $$mathcalLg(boldsymbolx, t) = int_0^infty g(boldsymbolx, t) e^-st dt = tildeg(boldsymbolx, s)$$ to your problem yields $$s^2 tildeu - tildeu_xx = tildef$$ You'll need to convert your boundary conditions as well and then solve the above ODE.
    – Mattos
    18 hours ago











  • The boundary conditions are just simply between 0 and 1 as opposed to infinity? I don't understand how your response is yielding a equation in terms of Lf(x) and Lu(x,t). I'm quite lost how to transform on these nonspecific functions.
    – FireMeUP
    18 hours ago










  • Mattos, where did you get g(x,t)?
    – FireMeUP
    15 hours ago










  • Can you explain where you difficulty is? Do you know what the Laplace transform is, and have you tried applying it?
    – Strants
    15 hours ago












up vote
-1
down vote

favorite
3









up vote
-1
down vote

favorite
3






3





Challenege Q



I am supposed to take the Laplace transform of the wave equation that yields a non-homogeneous ordinary differential equation in terms of $mathcalLf(x)$ and $mathcalLu(x,t)$ and its $x$-derivatives.



Can someone please explain the relationship between the two function, and how it's $x$-derivatives changes will be reflected in the function. This question was posed as a challenge question, and I am seeking some guidance.




differential-equations pde partial-derivative wave-equation initial-value-problems




share|cite|improve this question













Challenege Q



I am supposed to take the Laplace transform of the wave equation that yields a non-homogeneous ordinary differential equation in terms of $mathcalLf(x)$ and $mathcalLu(x,t)$ and its $x$-derivatives.



Can someone please explain the relationship between the two function, and how it's $x$-derivatives changes will be reflected in the function. This question was posed as a challenge question, and I am seeking some guidance.





differential-equations pde partial-derivative wave-equation initial-value-problems





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited 15 hours ago









Strants

5,05421536




5,05421536









asked 21 hours ago









FireMeUP

456




456











  • Here's a MathJax tutorial :)
    – Shaun
    19 hours ago










  • I'm not sure what your question is. Applying the Laplace transform $$mathcalLg(boldsymbolx, t) = int_0^infty g(boldsymbolx, t) e^-st dt = tildeg(boldsymbolx, s)$$ to your problem yields $$s^2 tildeu - tildeu_xx = tildef$$ You'll need to convert your boundary conditions as well and then solve the above ODE.
    – Mattos
    18 hours ago











  • The boundary conditions are just simply between 0 and 1 as opposed to infinity? I don't understand how your response is yielding a equation in terms of Lf(x) and Lu(x,t). I'm quite lost how to transform on these nonspecific functions.
    – FireMeUP
    18 hours ago










  • Mattos, where did you get g(x,t)?
    – FireMeUP
    15 hours ago










  • Can you explain where you difficulty is? Do you know what the Laplace transform is, and have you tried applying it?
    – Strants
    15 hours ago
















  • Here's a MathJax tutorial :)
    – Shaun
    19 hours ago










  • I'm not sure what your question is. Applying the Laplace transform $$mathcalLg(boldsymbolx, t) = int_0^infty g(boldsymbolx, t) e^-st dt = tildeg(boldsymbolx, s)$$ to your problem yields $$s^2 tildeu - tildeu_xx = tildef$$ You'll need to convert your boundary conditions as well and then solve the above ODE.
    – Mattos
    18 hours ago











  • The boundary conditions are just simply between 0 and 1 as opposed to infinity? I don't understand how your response is yielding a equation in terms of Lf(x) and Lu(x,t). I'm quite lost how to transform on these nonspecific functions.
    – FireMeUP
    18 hours ago










  • Mattos, where did you get g(x,t)?
    – FireMeUP
    15 hours ago










  • Can you explain where you difficulty is? Do you know what the Laplace transform is, and have you tried applying it?
    – Strants
    15 hours ago















Here's a MathJax tutorial :)
– Shaun
19 hours ago




Here's a MathJax tutorial :)
– Shaun
19 hours ago












I'm not sure what your question is. Applying the Laplace transform $$mathcalLg(boldsymbolx, t) = int_0^infty g(boldsymbolx, t) e^-st dt = tildeg(boldsymbolx, s)$$ to your problem yields $$s^2 tildeu - tildeu_xx = tildef$$ You'll need to convert your boundary conditions as well and then solve the above ODE.
– Mattos
18 hours ago





I'm not sure what your question is. Applying the Laplace transform $$mathcalLg(boldsymbolx, t) = int_0^infty g(boldsymbolx, t) e^-st dt = tildeg(boldsymbolx, s)$$ to your problem yields $$s^2 tildeu - tildeu_xx = tildef$$ You'll need to convert your boundary conditions as well and then solve the above ODE.
– Mattos
18 hours ago













The boundary conditions are just simply between 0 and 1 as opposed to infinity? I don't understand how your response is yielding a equation in terms of Lf(x) and Lu(x,t). I'm quite lost how to transform on these nonspecific functions.
– FireMeUP
18 hours ago




The boundary conditions are just simply between 0 and 1 as opposed to infinity? I don't understand how your response is yielding a equation in terms of Lf(x) and Lu(x,t). I'm quite lost how to transform on these nonspecific functions.
– FireMeUP
18 hours ago












Mattos, where did you get g(x,t)?
– FireMeUP
15 hours ago




Mattos, where did you get g(x,t)?
– FireMeUP
15 hours ago












Can you explain where you difficulty is? Do you know what the Laplace transform is, and have you tried applying it?
– Strants
15 hours ago




Can you explain where you difficulty is? Do you know what the Laplace transform is, and have you tried applying it?
– Strants
15 hours ago















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