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dy a) Show that the equation x² - 19y² 18xy = is homogeneous. dx The equation is homogeneous because the right-hand side can be written in terms of v = y/x as b) Solve the differential equation. NOTE: Use the positive number c for the constant of integration. The solution is given by y² = c) Draw a direction field and some integral curves. Are they symmetri- with respect to the origin? The integral curves Choose one symmetric with respect to the origin.

dy a) Show that the equation x² - 19y² 18xy = is homogeneous. dx The equation is homogeneous because the right-hand side can be written in terms of v = y/x as b) Solve the differential equation. NOTE: Use the positive number c for the constant of integration. The solution is given by y² = c) Draw a direction field and some integral curves. Are they symmetri- with respect to the origin? The integral curves Choose one symmetric with respect to the origin.

Advanced Engineering Mathematics
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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dy a) Show that the equation x² - 19y² 18xy = is homogeneous. dx The equation is homogeneous because the right-hand side can be written in terms of v = y/x as b) Solve the differential equation. NOTE: Use the positive number c for the constant of integration. The solution is given by y²: = c) Draw a direction field and some integral curves. Are they symmetric with respect to the origin? The integral curves Choose one symmetric with respect to the origin.
Transcribed Image Text:dy a) Show that the equation x² - 19y² 18xy = is homogeneous. dx The equation is homogeneous because the right-hand side can be written in terms of v = y/x as b) Solve the differential equation. NOTE: Use the positive number c for the constant of integration. The solution is given by y²: = c) Draw a direction field and some integral curves. Are they symmetric with respect to the origin? The integral curves Choose one symmetric with respect to the origin.
a) Show that the equation dy x² - 19y² 18xy = is homogeneous. dx The equation is homogeneous because the right-hand side can be written in terms of v = y/x as b) Solve the differential equation. NOTE: Use the positive number c for the constant of integration. The solution is given by y² = c) Draw a direction field and some integral curves. Are they symmetric with respect to the origin? The integral curves Choose one symmetric with resp are tin. are not
Transcribed Image Text:a) Show that the equation dy x² - 19y² 18xy = is homogeneous. dx The equation is homogeneous because the right-hand side can be written in terms of v = y/x as b) Solve the differential equation. NOTE: Use the positive number c for the constant of integration. The solution is given by y² = c) Draw a direction field and some integral curves. Are they symmetric with respect to the origin? The integral curves Choose one symmetric with resp are tin. are not
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