The solution of the differential equation dy/dx = x+y/x-y is Option 1: y = x/2_e(x^2 + y^2) + C : C is an arbitary constant Option 2: y = sqrt(x^2 + y^2) + C : C is an arbitrary constant Option 3: y = 1/2_e(x^2 + y^2) + c : C is an arbitrary constant Option 4: ^-1y/x = 1/2_e(x^2 + y^2) + C: C is an arbitrary constant

The answer is '^-1y/x = 1/2_e(x^2 + y^2) + C: C is an arbitrary constant'. View full solution:

The solution of the differential equation dy/dx = x+y/x-y is

^-1y/x = 1/2_e(x^2 + y^2) + C: C is an arbitrary constant

y = x/2_e(x^2 + y^2) + C : C is an arbitary constant

y = 1/2_e(x^2 + y^2) + c : C is an arbitrary constant

^-1y/x = 1/2_e(x^2 + y^2) + C: C is an arbitrary constant

Calculus > Differential Equations

Medium

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$y = \frac{x}{2}\log_e(x^2 + y^2) + C$ : C is an arbitary constant

$y = \sqrt{x^2 + y^2} + C$ : C is an arbitrary constant

$y = \frac{1}{2}\log_e(x^2 + y^2) + c$ : C is an arbitrary constant

$\tan^{-1}\frac{y}{x} = \frac{1}{2}\log_e(x^2 + y^2) + C$ : C is an arbitrary constant

✅ Correct Option: 4

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