Laplace from tables: e^(at), cos(bt), sin(bt).
\nrebelmaths
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\n(b) Using the tables, $L[e^{\\var{b}t}]=\\frac{1}{s-(\\var{b})}$
\n(c) Using the tables, $L[e^{\\var{c}t}+e^{\\var{d}t}]=\\frac{1}{s-(\\var{c})}+\\frac{1}{s-\\var{d}}$
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\n$L\\{e^{at}\\}=\\frac{1}{s-a}$
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", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "Note that the Laplace transform of $e^{at}$ is $\\frac{1}{s-a}$
\n$L\\{e^{at}\\}=\\frac{1}{s-a}$
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\n$L\\{f(t)+g(t)\\}=L\\{f(t)\\}+L\\{g(t)\\}$
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\nIn this example $b=\\var{a}$
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\nIn this example $b=\\var{b}$
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\nIn the first part $b=\\frac{1}{\\var{a}}$ and in the second part $b=\\frac{1}{\\var{b}}$
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