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Sum

**Solve the following differential equation:**

`cos "x" * cos "y" "dy" - sin "x" * "sin y" "dx" = 0`

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#### Solution

`cos "x" * cos "y" "dy" - sin "x" * "sin y" "dx" = 0`

`"cos y"/"sin y" "dy" - "sin x"/"cos x" "dx" = 0`

Integrating both sides, we get

`int cot"y" "dy" - int "tan x" "dx" = "c"_1`

∴ `log |sin "y"| - [- log |sec "x"|] = log "c",` where c_{1} = log c

∴ `log |sin "y"| + log |sec "x"| = log "c"`

∴ `log |sin "y" * sec "x"| = log "c"`

∴ `sin "y" * cos "x" = "c"`

This is the general solution.

Concept: Formation of Differential Equations

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