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x dy + y dx = 0 5. (3x²y² + 2y³ - 4y) dx + (2x³y + 6xy² - 4x) dy = 0

x dy + y dx = 0 5. (3x²y² + 2y³ - 4y) dx + (2x³y + 6xy² - 4x) 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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Solve using exact DE Plz answer the question in 20 minutes it's very urgent plz and last 2 parts only question 4 and 5
1. (2xy + x²) dy + (2xy + y²) dx = 0 0000 A *A*3. (3x²y³ +3 sin x + 4y) dx + (3x³y² + 4x) dy = 0 x dy + y dx = 0 5. (3x²y² + 2y³ – 4y) dx + (2x³y + 6xy² − 4x) dy = 0 2. (3x² + 2xy) dx + (x²) dy = 0
Transcribed Image Text:1. (2xy + x²) dy + (2xy + y²) dx = 0 0000 A *A*3. (3x²y³ +3 sin x + 4y) dx + (3x³y² + 4x) dy = 0 x dy + y dx = 0 5. (3x²y² + 2y³ – 4y) dx + (2x³y + 6xy² − 4x) dy = 0 2. (3x² + 2xy) dx + (x²) dy = 0
Expert Solution
Part 4

Given :

4. xdy+ydx=0

Comparing above to Mdx+Ndy=0, we get

             M=y, My=1 and N=x, Nx=1

Clearly, My=1=Nx

The differential equation is exact. Hence the general solution is

     ∫M·dx+∫ (terms not containing x)N·dy=C⇒∫y dx +∫0 dx =C⇒xy=C

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