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5. Solve the equation using homogeneous equation xy dx – (x² + 3y²)dy = 0. 6. Solve the equation using exact equation (x + y)dx + (x – y)dy= 0. 7. Solve the equation using exact equation (6x +y²)dx + y(2x – 3y)dy = 0.

5. Solve the equation using homogeneous equation xy dx – (x² + 3y²)dy = 0. 6. Solve the equation using exact equation (x + y)dx + (x – y)dy= 0. 7. Solve the equation using exact equation (6x +y²)dx + y(2x – 3y)dy = 0.

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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Direction: Solve the following. Show your complete solution in each problem. 1. Solve the equation using variable separable dr = -4rt, when t= 0, r = r . dt 2. Solve the equation using variable separable 2xy y' = 1 + y², when x = 2,y = 3. 3. Solve the equation using homogeneous functions 3(3x² + y²)dx – 2xy dy = 0. 4. Solve the equation using homogeneous equation (x– 2y)dx+(2x + y)dy=0. 5. Solve the equation using homogeneous equation xy dx – (x² + 3y²)dy = 0. 6. Solve the equation using exact equation (x + y)dx + (x – y)dy = 0. 7. Solve the equation using exact equation (6x +y²)dx + y(2x – 3y)dy = 0. 8. Solve the equation using exact equation (2xy – 3x²)dx + (x² + y)dy = 0. 9. Solve the equation using linear equation (x5 + 3y) dx – x dy = 0. 10. Solve the equation using linear equation 2(2xy+4y – 3)dx+ (x+2)²dy = 0.
Transcribed Image Text:Direction: Solve the following. Show your complete solution in each problem. 1. Solve the equation using variable separable dr = -4rt, when t= 0, r = r . dt 2. Solve the equation using variable separable 2xy y' = 1 + y², when x = 2,y = 3. 3. Solve the equation using homogeneous functions 3(3x² + y²)dx – 2xy dy = 0. 4. Solve the equation using homogeneous equation (x– 2y)dx+(2x + y)dy=0. 5. Solve the equation using homogeneous equation xy dx – (x² + 3y²)dy = 0. 6. Solve the equation using exact equation (x + y)dx + (x – y)dy = 0. 7. Solve the equation using exact equation (6x +y²)dx + y(2x – 3y)dy = 0. 8. Solve the equation using exact equation (2xy – 3x²)dx + (x² + y)dy = 0. 9. Solve the equation using linear equation (x5 + 3y) dx – x dy = 0. 10. Solve the equation using linear equation 2(2xy+4y – 3)dx+ (x+2)²dy = 0.
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