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Choose the correct alternative. The solution of xdydx=y log y is - Mathematics and Statistics

MCQ

Choose the correct alternative.

The solution of `x dy/dx = y` log y is

Options

  • y = aex

  • y = be2x

  • y = be-2x

  • y = eax

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Solution

The solution of `x dy/dx = y` log y is y = eax

`x dy/dx = y` log y

∴ `dy/(ylogy) = dx/x`

Integrating on both sides, we get

`int dy/(y logy) = int 1/x dx`

∴ log log(y)= log x + log a

∴ log log(y)= log xa

∴ log(y)= ax

∴ y = eax

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 1.07 | Page 172
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