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What is the solution of dy/dx = (6x + 9y – 7)/(2x + 3y – 6)?
- a)3x – y + log|2x + 3y – 3| = -c/3
- b)3x – y + log|2x + 3y – 3| = c/3
- c)3x + y + log|2x + 3y – 3| = -c/3
- d)3x – y – log|2x + 3y – 3| = c/3
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
What is the solution of dy/dx = (6x + 9y – 7)/(2x + 3y – 6...
The given differential equation is dy/dx = 6x - 9y.
To solve this equation, we need to separate the variables and integrate both sides.
Rearranging the equation, we have dy/dx + 9y = 6x.
To separate the variables, we can multiply both sides by dx:
dy + 9y dx = 6x dx.
Now, we integrate both sides:
∫(dy + 9y dx) = ∫(6x dx).
Integrating, we get:
y + 9∫(y dx) = 3x^2 + C, where C is the constant of integration.
Now, we need to evaluate the integral on the left side. Since we are integrating with respect to x, y is treated as a constant. Thus, ∫(y dx) = yx.
Substituting this back into the equation, we have:
y + 9yx = 3x^2 + C.
This is the general solution to the given differential equation.
To solve this equation, we need to separate the variables and integrate both sides.
Rearranging the equation, we have dy/dx + 9y = 6x.
To separate the variables, we can multiply both sides by dx:
dy + 9y dx = 6x dx.
Now, we integrate both sides:
∫(dy + 9y dx) = ∫(6x dx).
Integrating, we get:
y + 9∫(y dx) = 3x^2 + C, where C is the constant of integration.
Now, we need to evaluate the integral on the left side. Since we are integrating with respect to x, y is treated as a constant. Thus, ∫(y dx) = yx.
Substituting this back into the equation, we have:
y + 9yx = 3x^2 + C.
This is the general solution to the given differential equation.
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Community Answer
What is the solution of dy/dx = (6x + 9y – 7)/(2x + 3y – 6...
dy/dx = (6x + 9y – 7)/(2x + 3y – 6)
So, dy/dx = (3(2x + 3y) – 7)/(2x + 3x – 6) ……….(1)
Now, we put, 2x + 3y = z
Therefore, 2 + 3dy/dx = dz/dx [differentiating with respect to x]
Or, dy/dx = 1/3(dz/dx – 2)
Therefore, from (1) we get,
1/3(dz/dx – 2) = (3z – 7)/(z – 6)
Or, dz/dx = 2 + (3(3z – 7))/(z – 6)
= 11(z – 3)/(z – 6)
Or, (z – 6)/(z – 3) dz = 11 dx
Or, ∫(z – 6)/(z – 3) dz = ∫11 dx
Or, ∫(1 – 3/(z – 3)) dz = 11x + c
Or, z – log |z – 3| = 11x + c
Or, 2x + 3y – 11x – 3log|2x + 3y -3| = c
Or, 3y – 9x – 3log|2x + 3y – 3| = c
Or, 3x – y + log|2x + 3y – 3| = -c/3
So, dy/dx = (3(2x + 3y) – 7)/(2x + 3x – 6) ……….(1)
Now, we put, 2x + 3y = z
Therefore, 2 + 3dy/dx = dz/dx [differentiating with respect to x]
Or, dy/dx = 1/3(dz/dx – 2)
Therefore, from (1) we get,
1/3(dz/dx – 2) = (3z – 7)/(z – 6)
Or, dz/dx = 2 + (3(3z – 7))/(z – 6)
= 11(z – 3)/(z – 6)
Or, (z – 6)/(z – 3) dz = 11 dx
Or, ∫(z – 6)/(z – 3) dz = ∫11 dx
Or, ∫(1 – 3/(z – 3)) dz = 11x + c
Or, z – log |z – 3| = 11x + c
Or, 2x + 3y – 11x – 3log|2x + 3y -3| = c
Or, 3y – 9x – 3log|2x + 3y – 3| = c
Or, 3x – y + log|2x + 3y – 3| = -c/3
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What is the solution of dy/dx = (6x + 9y – 7)/(2x + 3y – 6)?a)3x – y + log|2x + 3y – 3| = -c/3b)3x – y + log|2x + 3y – 3| = c/3c)3x + y + log|2x + 3y – 3| = -c/3d)3x – y – log|2x + 3y – 3| = c/3Correct answer is option 'A'. Can you explain this answer? for Class 12 2025 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about What is the solution of dy/dx = (6x + 9y – 7)/(2x + 3y – 6)?a)3x – y + log|2x + 3y – 3| = -c/3b)3x – y + log|2x + 3y – 3| = c/3c)3x + y + log|2x + 3y – 3| = -c/3d)3x – y – log|2x + 3y – 3| = c/3Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 12 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the solution of dy/dx = (6x + 9y – 7)/(2x + 3y – 6)?a)3x – y + log|2x + 3y – 3| = -c/3b)3x – y + log|2x + 3y – 3| = c/3c)3x + y + log|2x + 3y – 3| = -c/3d)3x – y – log|2x + 3y – 3| = c/3Correct answer is option 'A'. Can you explain this answer?.
What is the solution of dy/dx = (6x + 9y – 7)/(2x + 3y – 6)?a)3x – y + log|2x + 3y – 3| = -c/3b)3x – y + log|2x + 3y – 3| = c/3c)3x + y + log|2x + 3y – 3| = -c/3d)3x – y – log|2x + 3y – 3| = c/3Correct answer is option 'A'. Can you explain this answer? for Class 12 2025 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about What is the solution of dy/dx = (6x + 9y – 7)/(2x + 3y – 6)?a)3x – y + log|2x + 3y – 3| = -c/3b)3x – y + log|2x + 3y – 3| = c/3c)3x + y + log|2x + 3y – 3| = -c/3d)3x – y – log|2x + 3y – 3| = c/3Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 12 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the solution of dy/dx = (6x + 9y – 7)/(2x + 3y – 6)?a)3x – y + log|2x + 3y – 3| = -c/3b)3x – y + log|2x + 3y – 3| = c/3c)3x + y + log|2x + 3y – 3| = -c/3d)3x – y – log|2x + 3y – 3| = c/3Correct answer is option 'A'. Can you explain this answer?.
Solutions for What is the solution of dy/dx = (6x + 9y – 7)/(2x + 3y – 6)?a)3x – y + log|2x + 3y – 3| = -c/3b)3x – y + log|2x + 3y – 3| = c/3c)3x + y + log|2x + 3y – 3| = -c/3d)3x – y – log|2x + 3y – 3| = c/3Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 12.
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