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(6) Show that the differential equation (3ry + y*)dr + (r² + ry)dy = 0 is homoge- neous; solve it and show that its the solution is 2r*y+r*y = c. Find the integrating = C.

(6) Show that the differential equation (3ry + y*)dr + (r² + ry)dy = 0 is homoge- neous; solve it and show that its the solution is 2r*y+r*y = c. Find the integrating = C.

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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Question

Solve the following differential equations

**Problem 6: Homogeneous Differential Equation** **Task**: Show that the differential equation \((3xy + y^2)dx + (x^2 + xy)dy = 0\) is homogeneous. Solve it and demonstrate that the solution is \(2x^3y + x^2y^2 = c\). **Instructions**: 1. Confirm that the given differential equation is homogeneous. 2. Solve the equation. 3. Verify the solution by showing the result is \(2x^3y + x^2y^2 = c\). **Additional Task**: Without solving, find the integrating factor for the following equations.
Transcribed Image Text:**Problem 6: Homogeneous Differential Equation** **Task**: Show that the differential equation \((3xy + y^2)dx + (x^2 + xy)dy = 0\) is homogeneous. Solve it and demonstrate that the solution is \(2x^3y + x^2y^2 = c\). **Instructions**: 1. Confirm that the given differential equation is homogeneous. 2. Solve the equation. 3. Verify the solution by showing the result is \(2x^3y + x^2y^2 = c\). **Additional Task**: Without solving, find the integrating factor for the following equations.
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