CBSE Class 12 Sample Paper for 2023 Boards

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Question 29 (Choice 1) - CBSE Class 12 Sample Paper for 2023 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at August 2, 2026 by

Solve the differential equation: ydx+(x-y 2 )dy=0

[Class 12] Solve differential equation: 𝑦𝑑π‘₯ + (π‘₯ βˆ’ y^2)𝑑𝑦 = 0 - CBSE Class 12 Sample Paper for 2023 Boards

part 2 - Question 29 (Choice 1) - CBSE Class 12 Sample Paper for 2023 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12
part 3 - Question 29 (Choice 1) - CBSE Class 12 Sample Paper for 2023 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12

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Question 29 (Choice 1) Solve the differential equation: 𝑦𝑑π‘₯+(π‘₯βˆ’π‘¦^2 )𝑑𝑦=0 For equation 𝑦𝑑π‘₯+(π‘₯βˆ’π‘¦^2 )𝑑𝑦=0 We observe that we cannot use variable separation method Let’s try to put in the form π’…π’š/𝒅𝒙 + Py = Q or 𝒅𝒙/π’…π’š + P1 x = Q1 Now, y dx + (x βˆ’ y2) dy = 0 y dx = βˆ’ (x βˆ’ y2)dy π’…π’š/𝒅𝒙 = (βˆ’π’š)/(π’™βˆ’π’š^𝟐 ) This is not of the form 𝑑𝑦/𝑑π‘₯ + Py = Q Thus, let’s find 𝒅𝒙/π’…π’š 𝑑π‘₯/𝑑𝑦 = (𝑦^2 βˆ’ π‘₯)/𝑦 𝑑π‘₯/𝑑𝑦 = y βˆ’ π‘₯/𝑦 𝒅𝒙/π’…π’š + 𝒙/π’š = y Comparing with 𝒅𝒙/π’…π’š + P1 x = Q1 ∴ P1 = 1/𝑦 &. Q1 = y Finding Integrating factor, IF = 𝑒^∫1▒〖𝑝1 𝑑𝑦〗 = 𝑒^∫1▒𝑑𝑦/𝑦 = 𝒆^π’π’π’ˆβ‘π’š = y Solution is x (IF) = ∫1β–’γ€–(π‘ΈπŸ Γ— 𝑰𝑭)π’…π’š+𝒄〗 π‘₯𝑦=∫1▒〖𝑦 Γ— 𝑦 𝑑𝑦+𝑐〗 π’™π’š= ∫1β–’γ€–π’š^𝟐 π’…π’š+𝒄〗 π’™π’š= π’š^πŸ‘/πŸ‘+π‘ͺ

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