Solve the following differential equation: dydxxylog (dydx)=2x+3y - Mathematics and Statistics

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Sum

Solve the following differential equation:

`log  ("dy"/"dx") = 2"x" + 3"y"`

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Solution

`log  ("dy"/"dx") = 2"x" + 3"y"`

∴ `"dy"/"dx" = "e"^("2x" + "3y") = "e"^"2x"."e"^"3y"`

∴ `1/"e"^"3y" "dy" = "e"^"2x" "dx"`

Integrating both sides, we get

`int "e"^-"3y" "dy" = int "e"^"2x' "dx"`

∴ `int "e"^-3"y" "dy" = int "e"^"2x" "dx"`

∴ `("e"^(- "3y"))/-3 = "e"^"2x"/2 + "c"_1`

∴ `2"e"^-"3y" = - 3"e"^"2x" + 6"c"_1`

∴ `2"e"^-"3y" + 3"e"^"2x" = "c"`, where c = 6c1

This is the general solution.

Concept: Formation of Differential Equations
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Chapter 6: Differential Equations - Miscellaneous exercise 2 [Page 217]

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Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 6 Differential Equations
Miscellaneous exercise 2 | Q 5.1 | Page 217

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