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Solution of (x+y-1) dx+(2x+2y-3) dy = 0 is
- a)y+x+log (x+y-2)=c
- b)y+2x+log (x+y-2)=c
- c)2y+x+log(x+y-2)=c
- d)2y+2x+log(x+y-2)=c
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Solution of (x+y-1) dx+(2x+2y-3) dy = 0 isa)y+x+log (x+y-2)=cb)y+2x+lo...
Given Differential Equation:
The given differential equation is: (x+y-1) dx + (2x+2y-3) dy = 0
Solution:
Step 1: Integration
To solve the given differential equation, we first need to integrate both sides with respect to x and y.
Integrating the given equation:
∫(x+y-1) dx + ∫(2x+2y-3) dy = 0
Integrating the terms separately:
∫(x+y-1) dx = x^2/2 + xy - x + c1
∫(2x+2y-3) dy = x^2 + xy - 3y + c2
Step 2: Simplification
After integrating, we get:
(x^2/2 + xy - x) + (x^2 + xy - 3y) = c
Combining like terms:
x^2/2 + x^2 + 2xy - x - 3y = c
3x^2 + 4xy - 6y = 2c
Step 3: Final Solution
Rearranging the terms, we get:
2y + x + log(x+y-2) = c
Explanation of the Correct Answer:
The correct answer is option 'c' which matches the final solution obtained in the above steps. The solution 2y + x + log(x+y-2) = c is derived from integrating the given differential equation and simplifying the terms. This solution satisfies the given differential equation and matches the form provided in option 'c'.
The given differential equation is: (x+y-1) dx + (2x+2y-3) dy = 0
Solution:
Step 1: Integration
To solve the given differential equation, we first need to integrate both sides with respect to x and y.
Integrating the given equation:
∫(x+y-1) dx + ∫(2x+2y-3) dy = 0
Integrating the terms separately:
∫(x+y-1) dx = x^2/2 + xy - x + c1
∫(2x+2y-3) dy = x^2 + xy - 3y + c2
Step 2: Simplification
After integrating, we get:
(x^2/2 + xy - x) + (x^2 + xy - 3y) = c
Combining like terms:
x^2/2 + x^2 + 2xy - x - 3y = c
3x^2 + 4xy - 6y = 2c
Step 3: Final Solution
Rearranging the terms, we get:
2y + x + log(x+y-2) = c
Explanation of the Correct Answer:
The correct answer is option 'c' which matches the final solution obtained in the above steps. The solution 2y + x + log(x+y-2) = c is derived from integrating the given differential equation and simplifying the terms. This solution satisfies the given differential equation and matches the form provided in option 'c'.
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Solution of (x+y-1) dx+(2x+2y-3) dy = 0 isa)y+x+log (x+y-2)=cb)y+2x+log (x+y-2)=cc)2y+x+log(x+y-2)=cd)2y+2x+log(x+y-2)=cCorrect answer is option 'C'. Can you explain this answer?
Question Description
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