Find the general solution of the following differential equation:

CBSE Sample Question Paper, Class 12 Mathematics Term 2 Question - Find the general solution of the following differential equation:

By
Komal Kohli
-

Find the general solution of the following differential equation:

Answer.

π‘™π‘œπ‘”|π‘π‘œπ‘ π‘’π‘π‘£ βˆ’ π‘π‘œπ‘‘π‘£| = βˆ’π‘™π‘œπ‘”|π‘₯| + π‘™π‘œπ‘”πΎ,𝐾 > 0 (Here, π‘™π‘œπ‘”πΎ is an arbitrary
constant.)
β‡’ π‘™π‘œπ‘”|(π‘π‘œπ‘ π‘’π‘π‘£ βˆ’ π‘π‘œπ‘‘π‘£)π‘₯| = π‘™π‘œπ‘”πΎ
β‡’ |(π‘π‘œπ‘ π‘’π‘π‘£ βˆ’ π‘π‘œπ‘‘π‘£)π‘₯| = 𝐾
β‡’ (π‘π‘œπ‘ π‘’π‘π‘£ βˆ’ π‘π‘œπ‘‘π‘£)π‘₯ = ±𝐾
β‡’ (π‘π‘œπ‘ π‘’π‘ 𝑦/π‘₯βˆ’ π‘π‘œπ‘‘ 𝑦/π‘₯) π‘₯ = 𝐢, which is the required general solution.

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