Education Blogs Find the general solution of the following differential equation:

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:

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May 18, 2022

Find the general solution of the following differential equation:

Answer.

𝑙𝑜𝑔|𝑐𝑜𝑠𝑒𝑐𝑣 − 𝑐𝑜𝑡𝑣| = −𝑙𝑜𝑔|𝑥| + 𝑙𝑜𝑔𝐾,𝐾 > 0 (Here, 𝑙𝑜𝑔𝐾 is an arbitrary
constant.)
⇒ 𝑙𝑜𝑔|(𝑐𝑜𝑠𝑒𝑐𝑣 − 𝑐𝑜𝑡𝑣)𝑥| = 𝑙𝑜𝑔𝐾
⇒ |(𝑐𝑜𝑠𝑒𝑐𝑣 − 𝑐𝑜𝑡𝑣)𝑥| = 𝐾
⇒ (𝑐𝑜𝑠𝑒𝑐𝑣 − 𝑐𝑜𝑡𝑣)𝑥 = ±𝐾
⇒ (𝑐𝑜𝑠𝑒𝑐 𝑦/𝑥− 𝑐𝑜𝑡 𝑦/𝑥) 𝑥 = 𝐶, which is the required general solution.