Is it separable, homogeneous or linear?

Calculus Level 4

y d x + x d y ( 1 + x y ) = 0 y dx + x dy {(1+xy)} = 0 has general solution of form ( Just after integrating) :

Algebraic function = logarithmic function + K Logarithmic function = logarithmic function + K Exponential function = Inverse trigonometric function + K Inverse Trigonometric function = logarithmic function + K Inverse trigonometric function = Inverse trigonometric function + K Algebraic function + K = 0 Algebraic function + Algebraic function = exponential function + K Algebraic function = algebraic function + K

Sachin Vishwakarma by Sachin Vishwakarma , 22, India

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1 solution

Resolve it as ( y + x d y d x ) d x x 2 y 2 = − 1 y d y \frac{(y + x \frac{dy}{dx}) dx }{x^2 y^2} = - \frac{1}{y} dy

After integrating both side :

1 x y = ln ⁡ y + K \frac{1}{xy} = \ln{y} + K

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