Solve the following differential equation: ex + 2ydxdy2ex + 2ydx-3dy=0 - Mathematics and Statistics

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Sum

Solve the following differential equation:

`2"e"^("x + 2y") "dx" - 3"dy" = 0`

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Solution

`2"e"^("x + 2y") "dx" - 3"dy" = 0`

∴ `2"e"^"x" * "e"^"2y" "dx" - 3"dy" = 0`

∴ `2"e"^"x" "dx" - 3/"e"^"2y" "dy" = 0` 

Integrating both sides, we get

`2 int "e"^"x" "dx" - 3 int "e"^(-2"y") "dy" = "c"_1`

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

∴ `4"e"^"x" + 3"e"^(- 2"y") = 2"c"_1`

∴ `4"e"^"x" + 3"e"^(- 2"y") = "c"`, where c = 2c1.

This is the general solution.

Concept: Formation of Differential Equations
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Chapter 6: Differential Equations - Exercise 6.3 [Page 201]

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