CBSE Class 12 Sample Paper for 2023 Boards

Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

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

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Question 29 (Choice 1) Solve the differential equation: π¦ππ₯+(π₯βπ¦^2 )ππ¦=0 For equation π¦ππ₯+(π₯βπ¦^2 )ππ¦=0 We observe that we cannot use variable separation method Letβs try to put in the form ππ/ππ + Py = Q or ππ/ππ + P1 x = Q1 Now, y dx + (x β y2) dy = 0 y dx = β (x β y2)dy ππ/ππ = (βπ)/(πβπ^π ) This is not of the form ππ¦/ππ₯ + Py = Q Thus, letβs find ππ/ππ ππ₯/ππ¦ = (π¦^2 β π₯)/π¦ ππ₯/ππ¦ = y β π₯/π¦ ππ/ππ + π/π = y Comparing with ππ/ππ + P1 x = Q1 β΄ P1 = 1/π¦ &. Q1 = y Finding Integrating factor, IF = π^β«1βγπ1 ππ¦γ = π^β«1βππ¦/π¦ = π^πππβ‘π = y Solution is x (IF) = β«1βγ(πΈπ Γ π°π­)ππ+πγ π₯π¦=β«1βγπ¦ Γ π¦ ππ¦+πγ ππ= β«1βγπ^π ππ+πγ ππ= π^π/π+πͺ