4. (y + y + 1) dx + x(x-3y²-1) dy 0 y-xy + y +1=x ans. 5. y = ax + by + c ans. b²y = C₁ ex-abx - a - bc 6. (2x³y² + 4x²y + 2xy² + xy + 2y) dx + 2(y + xy + x) dy = 0 ans. (2x²y² + 4xy + y^) exp (x²) = c 7. (x² + y² + x) dx + xy dy = 0 ans. x²(3x² + 4x + 6y²) = c 8. [2xy exp(y) + 2xy + y) dx + [x²y'exp(y)-x²y2²-3x) dy = 0 ans. x²y' exp(y) + x³y² + x = cy³
4. (y + y + 1) dx + x(x-3y²-1) dy 0 y-xy + y +1=x ans. 5. y = ax + by + c ans. b²y = C₁ ex-abx - a - bc 6. (2x³y² + 4x²y + 2xy² + xy + 2y) dx + 2(y + xy + x) dy = 0 ans. (2x²y² + 4xy + y^) exp (x²) = c 7. (x² + y² + x) dx + xy dy = 0 ans. x²(3x² + 4x + 6y²) = c 8. [2xy exp(y) + 2xy + y) dx + [x²y'exp(y)-x²y2²-3x) dy = 0 ans. x²y' exp(y) + x³y² + x = cy³
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
Answer 4-8 only
Transcribed Image Text:Chapter III. Additional Topics on t
PROBLEM SETS
Obtain the general solution.
dv = 0
5. y'= ax + by + c
ans.
4. (y + y + 1) dx + x(x-3y²-1) dy = 0
ans. y-xy + y + 1 = x
Equations of Order Or
b²y = C₁ ex-abx - a - bc
6. (2x³y² + 4x²y + 2xy² + xy + 2y) dx
+ 2(y + x²y + x) dy = 0
ans. (2x²y² + 4xy + y^) exp (x²) = c
7. (x² + y² + x) dx + xy dy = 0
ans. x² (3x² + 4x + 6y²) = c
8. [2xy exp(y) + 2xy + y) dx
+ [x²y'exp(y)-x²y²-3x) dy = 0
ans. x²y³ exp(y) + x³y² + x = cy³
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