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CBSE Class 12 Sample Paper for 2025 Boards
CBSE Class 12 Sample Paper for 2025 Boards
Last updated at Feb. 12, 2025 by Teachoo
Question 14 What is the general solution of the differential equation π^(π¦^β² )=π₯ ? (A) π¦=π₯logπ₯+π (B) π¦=π₯logπ₯βπ₯+π (C) π¦=π₯logπ₯+π₯+π (D) π¦=π₯+πGiven differential equation π^(π¦^β² )=π₯ Taking log both sides log(π^(π¦^β² ))=logβ‘π₯ π¦^β² Γ log e=logβ‘π₯ Since log e = 1 π¦^β²=πππβ‘π₯ ππ¦/ππ₯ =πππβ‘π₯ ππ¦/ππ₯ =πππβ‘π₯ ππ¦=πππβ‘π₯ ππ₯ Integrating both sides β«1βππ¦=β«1βγπππβ‘π₯ ππ₯γ π=β«1βγπππβ‘π π πγ Putting β«1βγπππβ‘π₯ ππ₯γ=π₯ logβ‘π₯βπ₯+πΆ π=π πππβ‘πβπ+πͺ So, the correct answer is (B)