Find the Jacobian of the transformation x = 5u + 6v, y = u² + 7v
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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![**Transcription for Educational Website**
**Problem Statement:**
Find the Jacobian of the transformation \( x = 5u + 6v, \, y = u^2 + 7v \).
**Expression:**
\[
\frac{\partial(x, y)}{\partial(y, v)} = 35 - 124
\]
**Error Message:**
*Syntax error: you gave an equation, not an expression. Syntax error. Check your variables - you might be using an incorrect one.*
**Explanation:**
This error occurs because the expected input is an expression involving the partial derivatives of \( x \) and \( y \) with respect to \( u \) and \( v \), not a solved equation. The Jacobian determinant should be expressed in terms of the partial derivatives:
\[
J = \begin{vmatrix}
\frac{\partial x}{\partial u} & \frac{\partial x}{\partial v} \\
\frac{\partial y}{\partial u} & \frac{\partial y}{\partial v}
\end{vmatrix}
\]
Ensure you are using the correct variables and have specified the transformation appropriately.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70224edc-49fe-4fc4-bb2a-6cba35fc14ef%2F068e2cc5-5926-4d09-ae25-4d082e0fe435%2Fo4ktc10j_processed.png&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website**
**Problem Statement:**
Find the Jacobian of the transformation \( x = 5u + 6v, \, y = u^2 + 7v \).
**Expression:**
\[
\frac{\partial(x, y)}{\partial(y, v)} = 35 - 124
\]
**Error Message:**
*Syntax error: you gave an equation, not an expression. Syntax error. Check your variables - you might be using an incorrect one.*
**Explanation:**
This error occurs because the expected input is an expression involving the partial derivatives of \( x \) and \( y \) with respect to \( u \) and \( v \), not a solved equation. The Jacobian determinant should be expressed in terms of the partial derivatives:
\[
J = \begin{vmatrix}
\frac{\partial x}{\partial u} & \frac{\partial x}{\partial v} \\
\frac{\partial y}{\partial u} & \frac{\partial y}{\partial v}
\end{vmatrix}
\]
Ensure you are using the correct variables and have specified the transformation appropriately.
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