Consider the following differential equation. dy =y6/7 dx Let f(x, y) = y6/7. Find the derivative of f. Əf = ду Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through a point (xo, Yo) in the region. O There is a unique solution in the entire xy-plane. O There is a unique solution in any rectangular region where y # 0. O There is a unique solution in any rectangular region where x ≥ 0. O There is a unique solution in any rectangular region where ly| < 1. O There is a unique solution in any rectangular region excluding the origin.
Consider the following differential equation. dy =y6/7 dx Let f(x, y) = y6/7. Find the derivative of f. Əf = ду Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through a point (xo, Yo) in the region. O There is a unique solution in the entire xy-plane. O There is a unique solution in any rectangular region where y # 0. O There is a unique solution in any rectangular region where x ≥ 0. O There is a unique solution in any rectangular region where ly| < 1. O There is a unique solution in any rectangular region excluding the origin.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![**Consider the following differential equation.**
\[
\frac{dy}{dx} = y^{6/7}
\]
**Let** \( f(x, y) = y^{6/7} \). **Find the derivative of** \( f \).
\[
\frac{\partial f}{\partial y} = \_\_\_\_
\]
**Determine a region of the** \( xy \)-**plane for which the given differential equation would have a unique solution whose graph passes through a point** \((x_0, y_0)\) **in the region.**
- \( \circ \) There is a unique solution in the entire \( xy \)-plane.
- \( \circ \) There is a unique solution in any rectangular region where \( y \neq 0 \).
- \( \circ \) There is a unique solution in any rectangular region where \( x \geq 0 \).
- \( \circ \) There is a unique solution in any rectangular region where \( |y| < 1 \).
- \( \circ \) There is a unique solution in any rectangular region excluding the origin.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed7b56a3-2e66-4877-848b-86d54658cb11%2Fa813c697-1d39-42a1-8035-bbafcedd8471%2Fx020d3_processed.png&w=3840&q=75)
Transcribed Image Text:**Consider the following differential equation.**
\[
\frac{dy}{dx} = y^{6/7}
\]
**Let** \( f(x, y) = y^{6/7} \). **Find the derivative of** \( f \).
\[
\frac{\partial f}{\partial y} = \_\_\_\_
\]
**Determine a region of the** \( xy \)-**plane for which the given differential equation would have a unique solution whose graph passes through a point** \((x_0, y_0)\) **in the region.**
- \( \circ \) There is a unique solution in the entire \( xy \)-plane.
- \( \circ \) There is a unique solution in any rectangular region where \( y \neq 0 \).
- \( \circ \) There is a unique solution in any rectangular region where \( x \geq 0 \).
- \( \circ \) There is a unique solution in any rectangular region where \( |y| < 1 \).
- \( \circ \) There is a unique solution in any rectangular region excluding the origin.
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