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What is the solution of (y(dy/dx) + 2x)2 = (y2 + 2x2)[1 + (dy/dx)2]?
- a)cx±1/√2 = y/x + √(y2 – 2x2)/x2
- b)cx±√2 = y/x + √(y2 + 2x2)/x2
- c)cx±1/2√2 = y/x + √(y2 – 2x2)/x2
- d)cx±1/√2 = y/x + √(y2 + 2x2)/x2
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
What is the solution of (y(dy/dx) + 2x)2= (y2+ 2x2)[1 + (dy/dx)2]?a)cx...
Here, y2(dy/dx)2 + 4x2 + 4xy(dy/dx) = (y2 + 2x2)[1 + (dy/dx)2]
⇒ dy/dx = y/x ± √(1/2(y/x)2) + 1
Let, y = vx
⇒ v + x dv/dx = v ± √(1/2(v)2) + 1
Integrating both sides,
±√dv/(√(1/2(v)2) + 1) = ∫dx/x
cx±1/√2 = y/x + √(y2 + 2x2)/x2
⇒ dy/dx = y/x ± √(1/2(y/x)2) + 1
Let, y = vx
⇒ v + x dv/dx = v ± √(1/2(v)2) + 1
Integrating both sides,
±√dv/(√(1/2(v)2) + 1) = ∫dx/x
cx±1/√2 = y/x + √(y2 + 2x2)/x2
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What is the solution of (y(dy/dx) + 2x)2= (y2+ 2x2)[1 + (dy/dx)2]?a)cx...
The given equation is:
(y(dy/dx) + 2x)^2 = (y^2 - 2x^2)(1 - (dy/dx)^2)
Expanding the left-hand side of the equation:
(y^2(dy/dx)^2 + 4xy(dy/dx) + 4x^2) = (y^2 - 2x^2)(1 - (dy/dx)^2)
Expanding the right-hand side of the equation:
y^2(dy/dx)^2 + 4xy(dy/dx) + 4x^2 = y^2 - 2x^2 - y^2(dy/dx)^2 + 2x^2(dy/dx)^2
Combining like terms:
2y^2(dy/dx)^2 + 6x^2(dy/dx) - 2x^2 = 0
Simplifying the equation:
y^2(dy/dx)^2 + 3x^2(dy/dx) - x^2 = 0
This is a quadratic equation in terms of (dy/dx). We can solve this equation using the quadratic formula:
(dy/dx) = (-3x^2 ± √(9x^4 + 4x^2y^2)) / 2y^2
Therefore, the solution is:
(dy/dx) = (-3x^2 ± √(9x^4 + 4x^2y^2)) / 2y^2
Thus, the solution of the given equation is:
(dy/dx) = (-3x^2 ± √(9x^4 + 4x^2y^2)) / 2y^2
Note that "c" is not the correct answer.
(y(dy/dx) + 2x)^2 = (y^2 - 2x^2)(1 - (dy/dx)^2)
Expanding the left-hand side of the equation:
(y^2(dy/dx)^2 + 4xy(dy/dx) + 4x^2) = (y^2 - 2x^2)(1 - (dy/dx)^2)
Expanding the right-hand side of the equation:
y^2(dy/dx)^2 + 4xy(dy/dx) + 4x^2 = y^2 - 2x^2 - y^2(dy/dx)^2 + 2x^2(dy/dx)^2
Combining like terms:
2y^2(dy/dx)^2 + 6x^2(dy/dx) - 2x^2 = 0
Simplifying the equation:
y^2(dy/dx)^2 + 3x^2(dy/dx) - x^2 = 0
This is a quadratic equation in terms of (dy/dx). We can solve this equation using the quadratic formula:
(dy/dx) = (-3x^2 ± √(9x^4 + 4x^2y^2)) / 2y^2
Therefore, the solution is:
(dy/dx) = (-3x^2 ± √(9x^4 + 4x^2y^2)) / 2y^2
Thus, the solution of the given equation is:
(dy/dx) = (-3x^2 ± √(9x^4 + 4x^2y^2)) / 2y^2
Note that "c" is not the correct answer.
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What is the solution of (y(dy/dx) + 2x)2= (y2+ 2x2)[1 + (dy/dx)2]?a)cx±1/√2= y/x + √(y2– 2x2)/x2b)cx±√2= y/x + √(y2+ 2x2)/x2c)cx±1/2√2= y/x + √(y2– 2x2)/x2d)cx±1/√2= y/x + √(y2+ 2x2)/x2Correct answer is option 'D'. Can you explain this answer?
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What is the solution of (y(dy/dx) + 2x)2= (y2+ 2x2)[1 + (dy/dx)2]?a)cx±1/√2= y/x + √(y2– 2x2)/x2b)cx±√2= y/x + √(y2+ 2x2)/x2c)cx±1/2√2= y/x + √(y2– 2x2)/x2d)cx±1/√2= y/x + √(y2+ 2x2)/x2Correct answer is option 'D'. Can you explain this answer? for Class 12 2024 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 (y(dy/dx) + 2x)2= (y2+ 2x2)[1 + (dy/dx)2]?a)cx±1/√2= y/x + √(y2– 2x2)/x2b)cx±√2= y/x + √(y2+ 2x2)/x2c)cx±1/2√2= y/x + √(y2– 2x2)/x2d)cx±1/√2= y/x + √(y2+ 2x2)/x2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the solution of (y(dy/dx) + 2x)2= (y2+ 2x2)[1 + (dy/dx)2]?a)cx±1/√2= y/x + √(y2– 2x2)/x2b)cx±√2= y/x + √(y2+ 2x2)/x2c)cx±1/2√2= y/x + √(y2– 2x2)/x2d)cx±1/√2= y/x + √(y2+ 2x2)/x2Correct answer is option 'D'. Can you explain this answer?.
What is the solution of (y(dy/dx) + 2x)2= (y2+ 2x2)[1 + (dy/dx)2]?a)cx±1/√2= y/x + √(y2– 2x2)/x2b)cx±√2= y/x + √(y2+ 2x2)/x2c)cx±1/2√2= y/x + √(y2– 2x2)/x2d)cx±1/√2= y/x + √(y2+ 2x2)/x2Correct answer is option 'D'. Can you explain this answer? for Class 12 2024 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 (y(dy/dx) + 2x)2= (y2+ 2x2)[1 + (dy/dx)2]?a)cx±1/√2= y/x + √(y2– 2x2)/x2b)cx±√2= y/x + √(y2+ 2x2)/x2c)cx±1/2√2= y/x + √(y2– 2x2)/x2d)cx±1/√2= y/x + √(y2+ 2x2)/x2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the solution of (y(dy/dx) + 2x)2= (y2+ 2x2)[1 + (dy/dx)2]?a)cx±1/√2= y/x + √(y2– 2x2)/x2b)cx±√2= y/x + √(y2+ 2x2)/x2c)cx±1/2√2= y/x + √(y2– 2x2)/x2d)cx±1/√2= y/x + √(y2+ 2x2)/x2Correct answer is option 'D'. Can you explain this answer?.
Solutions for What is the solution of (y(dy/dx) + 2x)2= (y2+ 2x2)[1 + (dy/dx)2]?a)cx±1/√2= y/x + √(y2– 2x2)/x2b)cx±√2= y/x + √(y2+ 2x2)/x2c)cx±1/2√2= y/x + √(y2– 2x2)/x2d)cx±1/√2= y/x + √(y2+ 2x2)/x2Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 12.
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What is the solution of (y(dy/dx) + 2x)2= (y2+ 2x2)[1 + (dy/dx)2]?a)cx±1/√2= y/x + √(y2– 2x2)/x2b)cx±√2= y/x + √(y2+ 2x2)/x2c)cx±1/2√2= y/x + √(y2– 2x2)/x2d)cx±1/√2= y/x + √(y2+ 2x2)/x2Correct answer is option 'D'. Can you explain this answer?, a detailed solution for What is the solution of (y(dy/dx) + 2x)2= (y2+ 2x2)[1 + (dy/dx)2]?a)cx±1/√2= y/x + √(y2– 2x2)/x2b)cx±√2= y/x + √(y2+ 2x2)/x2c)cx±1/2√2= y/x + √(y2– 2x2)/x2d)cx±1/√2= y/x + √(y2+ 2x2)/x2Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of What is the solution of (y(dy/dx) + 2x)2= (y2+ 2x2)[1 + (dy/dx)2]?a)cx±1/√2= y/x + √(y2– 2x2)/x2b)cx±√2= y/x + √(y2+ 2x2)/x2c)cx±1/2√2= y/x + √(y2– 2x2)/x2d)cx±1/√2= y/x + √(y2+ 2x2)/x2Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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