Advertisement Remove all ads

Solve the following differential equation: xydyxsin ydxcosx⋅cosy dy-sinx⋅sin ydx=0 - Mathematics and Statistics

Advertisement Remove all ads
Advertisement Remove all ads
Sum

Solve the following differential equation:

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

Advertisement Remove all ads

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 |cos "x"|] = log "c",`where c1 = log c

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

∴ `log |sin "y" * cos "x"| = log "c"`

∴ `sin "y" * cos "x" = "c"`

This is the general solution.

Concept: Formation of Differential Equations
  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×