Chapter 111. Additional Topics on Equations of Orde PROBLEM SETS Obtain the general solution. 1. y(x² + y) dx + x(x²-2y) dy = 0 ay(x²-y) = x 2. y(2x + y) dx + x(y²-x) dy = 0 x(x + y²) = cy ans. 3. vdx + 2(y-x) dy = 0 an x=y²³ (c- y²)

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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Chapter 111. Additional Topics on t
PROBLEM SETS
Obtain the general solution.
1. y(x² + y) dx + x(x-2y) dy = 0
ay(x²-y) = xx
2. y(2x + y) dx + x(y²-x) dy = 0
ans. x(x + y) = cy
3. vdx + 2(y-x) dy = 0
3. x=y² (c- y²)
4. (y + y + 1) dx + x(x-3y² - 1) dy = 0
ans. y - xy + y +1=x
5. y'= ax + by + c
ans.
Equations of Order Or
b²y = C₁ ex-abx - a - bc
6. (2x³y² + 4x²y + 2xy² + xy + 2y) dx
+ 2(y + x²y + x) dy = 0
ans. (2x³y² + 4xy + y^) exp (x²) = c
7. (x² + y² + x) dx + xy dy = 0
x² (3x² + 4x + 6y²) = c
ans.
8. [2xy exp(y) + 2xy + y) dx
+ [x²y'exp(y)-x²y²-3x) dy = 0
ans. x²y³ exp(y) + x³y² + x = cy³
Transcribed Image Text:Chapter 111. Additional Topics on t PROBLEM SETS Obtain the general solution. 1. y(x² + y) dx + x(x-2y) dy = 0 ay(x²-y) = xx 2. y(2x + y) dx + x(y²-x) dy = 0 ans. x(x + y) = cy 3. vdx + 2(y-x) dy = 0 3. x=y² (c- y²) 4. (y + y + 1) dx + x(x-3y² - 1) dy = 0 ans. y - xy + y +1=x 5. y'= ax + by + c ans. Equations of Order Or b²y = C₁ ex-abx - a - bc 6. (2x³y² + 4x²y + 2xy² + xy + 2y) dx + 2(y + x²y + x) dy = 0 ans. (2x³y² + 4xy + y^) exp (x²) = c 7. (x² + y² + x) dx + xy dy = 0 x² (3x² + 4x + 6y²) = c ans. 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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