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Choose the correct alternative. The differential equation of y = k1+k2x is - Mathematics and Statistics

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MCQ

Choose the correct alternative.

The differential equation of y = `k_1 + k_2/x` is

Options

  • `(d^2y)/dx^2 + 2 dy/dx = 0`

  • `x(d^2y)/dx^2 + 2 dy/dx = 0`

  • `(d^2y)/dx^2 -2 dy/dx = 0`

  • `x(d^2y)/dx^2 -2 dy/dx = 0`

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Solution

The differential equation of `y = k_1 + k_2/x` is `x(d^2y)/dx^2 + 2 dy/dx = 0`

Explanation

`y = k_1 + k_2/x`

∴ xy = xk1 + k2

Differentiating w.r.t. x, we get

`y+x dy/dx = k_1`

Again, differentiating w.r.t. x, we get

`dy/dx + dy/dx + x (d^2y)/dx^2 = 0`

∴ `x (d^2y)/dx^2 + 2 dy/dx = 0`

Concept: Differential Equations
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 8 Differential Equation and Applications
Miscellaneous Exercise 8 | Q 1.03 | Page 171
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