# Reduce the following differential equation to the variable separable form and hence solve: x - 2ydydxcos2(x - 2y)=1-2dydx - Mathematics and Statistics

Sum

Reduce the following differential equation to the variable separable form and hence solve:

cos^2 ("x - 2y") = 1 - 2 "dy"/"dx"

#### Solution

cos^2 ("x - 2y") = 1 - 2 "dy"/"dx"      .....(1)

Put x - 2y = u. Then 1 - 2 "dy"/"dx" = "du"/"dx"

∴ (1) becomes, cos^2 "u" = "du"/"dx"

∴ dx = 1/cos^2"u"du

Integrating both sides, we get

∫ dx = ∫ sec2u du

∴ x = tan u + c

∴ x = tan (x - 2y) + c

This is the general solution.

Concept: Formation of Differential Equations
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