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Most Important Selected Qs for JEE AdvancedMathematicsDifferential Equations

The differential equation of the curve for which intercept cut by any tangent on y -axis is equal to the length of the sub normal -

Options

  1. Ais linear
  2. Bis homogeneous of first degree
  3. Chas separable variables
  4. Dis of first order

Correct answer

D. is of first order

Step-by-step solution

Let y =f( x ) be the curve. Equation of tangent at (x, y) will be Y - y =f^ ( x )( X - x ) Intercept cut by the tangent on y -axis will be y-x f^ (x) so y-x f^ (x)=y d y d x d y d x = y x+y This is homogeneous equation of first degree & first order. Rewriting this equation d x d y - x y =1 which is a linear equation.

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