The general solution of the differential equation √(1+x²+y²+x²y²) + xy(dy/dx)=0 is: (where C is a constant of integration)
The general solution of the differential equation √(1+x²+y²+x²y²) + xy(dy/dx)=0 is: (where C is a constant of integration)
Option 1 -
√(1+y²) + √(1+x²) = (1/2)logₑ((√(1+x²)+1)/(√(1+x²)-1)) + C
Option 2 -
√(1+y²) - √(1+x²) = (1/2)logₑ((√(1+x²)+1)/(√(1+x²)-1)) + C
Option 3 -
√(1+y²) - √(1+x²) = (1/2)logₑ((√(1+x²)-1)/(√(1+x²)+1)) + C
Option 4 -
√(1+y²) + √(1+x²) = (1/2)logₑ((√(1+x²)-1)/(√(1+x²)+1)) + C
Asked by Shiksha User
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1 Answer
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Correct Option - 1
Detailed Solution:√ (1+x²) (1+y²) + xy (dy/dx)=0.
√ (1+x²)/x dx + √ (1+y²)/y dy = 0.
√ (1+x²)+½ln| (√ (1+x²)-1)/ (√ (1+x²)+1)|+√ (1+y²)=C.
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