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CBSE Class 12 Sample Paper for 2025 Boards
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CBSE Class 12 Sample Paper for 2025 Boards
Last updated at Oct. 3, 2024 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)