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Expert-verified Found in: Page 30 ### Fundamentals Of Differential Equations And Boundary Value Problems

Book edition 9th
Author(s) R. Kent Nagle, Edward B. Saff, Arthur David Snider
Pages 616 pages
ISBN 9780321977069 # The initial value problem $\frac{{{\bf{dx}}}}{{{\bf{dt}}}}{\bf{ = 3}}{{\bf{x}}^{\frac{{\bf{2}}}{{\bf{3}}}}}{\bf{,}}\;{\bf{x(0) = 1}}$ has a unique solution in some open interval around t = 0.

The given statement is true.

See the step by step solution

## Step 1: Finding partial derivatives

Since $\frac{{{\bf{dx}}}}{{{\bf{dt}}}}{\bf{ = 3}}{{\bf{x}}^{\frac{{\bf{2}}}{{\bf{3}}}}}$

Then$\frac{{\partial {\bf{f}}}}{{\partial {\bf{x}}}}{\bf{ = }}\frac{{\bf{2}}}{{\sqrt[{\bf{3}}]{{\bf{x}}}}}$

## Step 2: Checking the final result

Apply the initial conditions$x\left( 0 \right) = 1$

$\frac{{\partial f}}{{\partial x}}{\bf{ = }}\frac{{\bf{2}}}{{\bf{0}}}$

The result is infinite.

The given function is discontinuous a x = 0. So the function is not continuous in a rectangle containing the point (0,1).

Therefore, the statement is True. ### Want to see more solutions like these? 