Match the following:
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a. \(\frac{{{\partial ^2}u}}{{\partial {t^2}}} = C\frac{{{\partial ^2}u}}{{\partial {x^2}}}\) |
I. Two-dimensional Poisson equation |
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b. \(\frac{{\partial u}}{{\partial t}} = C\frac{{{\partial ^2}u}}{{\partial {x^2}}}\) |
II. One-dimensional wave equation |
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c. \(\frac{{{\partial ^2}u}}{{\partial {x^2}}} + \frac{{{\partial ^2}u}}{{\partial {y^2}}} = 0\) |
III. One-dimensional heat equation |
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d. \(\frac{{{\partial ^2}u}}{{\partial {x^2}}} + \frac{{{\partial ^2}a}}{{\partial y}} = f\left( {x,y} \right)\) |
IV. Two-dimensional Laplace equation |
1
a-II, b-III, c-I, d-IV
2
a-II, b-III, c-IV, d-I
3
a-IV, b-I, c-III, d-II
4
a-IV, b-III, c-II, d-I