Q12RP
Question
The initial value problem \[\frac{{{\bf{dx}}}}{{{\bf{dt}}}}{\bf{ = 3}}{{\bf{y}}^{\frac{{\bf{2}}}{{\bf{3}}}}}{\bf{,}}\;{\bf{y(2) = 1}}{{\bf{0}}^{{\bf{ - 100}}}}\]has a unique solution in some open interval around x = 2.
Step-by-Step Solution
Verified Answer
The given statement is true.
1Step 1: Finding partial derivatives
Since \[\frac{{{\bf{dx}}}}{{{\bf{dt}}}}{\bf{ = 3}}{{\bf{y}}^{\frac{{\bf{2}}}{{\bf{3}}}}}\]
Then\[\frac{{\partial {\bf{f}}}}{{\partial {\bf{y}}}}{\bf{ = }}\frac{{\bf{2}}}{{\sqrt[{\bf{3}}]{{\bf{y}}}}}\]
2Step 2: Checking the final result
The given function is continuous at x = 2.So the function is continuous at some open interval x = 2.
Therefore, the statement is true.
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