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AP EAMCET20227 Jul 2022Morning ShiftMathematicsDifferential EquationsActual

If a a₁ = b b₁ , then the substitution to be used to solve the differential equation d y d x = a x+b y+c a₁ x+b₁ y+c₁ by using separation of variables is

Options

  1. Ax=x+h, y=y+k
  2. Ba x+b y=z
  3. Cy=V(x) x
  4. Dx=a t, y=b t

Correct answer

B. a x+b y=z

Step-by-step solution

If however a a₁ = b b₁ =m (say), then the differential equation becomes of the form d y d x = m (a₁ x+b₁ y )+C a₁ x+b₁ y+C₁ . To solve such a differential equation put u=a₁ x+b₁ y , get rid of y and then the transformed equation will be such that the variables are separable.

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