1. (cos 2y-3x²y²) dx + (cos 2y - 2x sin 2y - 2x³y)dy = 0 - 2. [x√x² + y² − y]dx+ (y√x² + y² − x)dy = 0 - 3. (xy² + x-2y+3)dx + x²ydy = 2(x + y)dy when x = 1, y = 1
1. (cos 2y-3x²y²) dx + (cos 2y - 2x sin 2y - 2x³y)dy = 0 - 2. [x√x² + y² − y]dx+ (y√x² + y² − x)dy = 0 - 3. (xy² + x-2y+3)dx + x²ydy = 2(x + y)dy when x = 1, y = 1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Differentiate using exact differential equation
![1. (cos 2y-3x²y²) dx
+(cos 2y - 2x sin 2y - 2x³y)dy = 0
2. (x √ x² + y² = y) dx + (y√/x² + y² − x)dy=0
3. (xy² + x-2y+3)dx + x² ydy = 2(x + y)dy
when x = 1, y = 1
4. (y² cos x -3x²y - 2x)dx
y(0)= e
+(2 y sin x-x³ + ln y)dy = 0
5. (1−xy) ² dx + [y² + x² (1− xy) ² ]dy = 0
when x = 4, y = 1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd26587ce-7f5a-4c4f-81d1-cddd9990560b%2F416a2aa6-be73-485c-bff3-e8d310772d61%2Fhpsg61_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. (cos 2y-3x²y²) dx
+(cos 2y - 2x sin 2y - 2x³y)dy = 0
2. (x √ x² + y² = y) dx + (y√/x² + y² − x)dy=0
3. (xy² + x-2y+3)dx + x² ydy = 2(x + y)dy
when x = 1, y = 1
4. (y² cos x -3x²y - 2x)dx
y(0)= e
+(2 y sin x-x³ + ln y)dy = 0
5. (1−xy) ² dx + [y² + x² (1− xy) ² ]dy = 0
when x = 4, y = 1
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