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Question
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.
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