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MHT CET202617 April 2026Evening ShiftMathematicsDifferential EquationsActual

The general solution of the differential equations dy dx = (9x + y + 5)^2 is...

Options

  1. A⁻¹ ( 9x + y + 5 2 ) = -2x + c
  2. B⁻¹ ( 9x + y + 5 2 ) = 2x + c
  3. C⁻¹ ( 9x + y + 5 3 ) = -3x + c
  4. D⁻¹ ( 9x + y + 5 3 ) = 3x + c

Correct answer

D. ⁻¹ ( 9x + y + 5 3 ) = 3x + c

Step-by-step solution

Let 9x + y + 5 = v Differentiating with respect to x : 9 + dy dx = dv dx dy dx = dv dx - 9 Substituting this in the given differential equation: dv dx - 9 = v^2 dv dx = v^2 + 9 dv v^2 + 9 = dx Integrating both sides: dv v^2 + 3^2 = dx 1 3 ⁻¹ ( v 3 ) = x + c₁ ⁻¹ ( v 3 ) = 3x + 3c₁ Substituting v = 9x + y + 5 and letting 3c₁ = c : ⁻¹ ( 9x + y + 5 3 ) = 3x + c Answer: ⁻¹ ( 9x + y + 5 3 ) = 3x + c

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