CBSE Class 12 Sample Paper for 2021 Boards

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

## Find the general solution of the following differential equation: π₯ ππ¦ β (π¦ + 2π₯ 2 )ππ₯ = 0

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Question 35 Find the general solution of the following differential equation: π₯ ππ¦ β (π¦ + 2π₯2 )ππ₯ = 0 Given π₯ ππ¦ = (π¦ + 2π₯2 )ππ₯ ππ¦/ππ₯=(π¦ + 2π₯^2)/π₯ ππ¦/ππ₯=π¦/π₯+2π₯ ππ/ππβπ/π=ππ Comparing with ππ/ππ + Py = Q β΄ P = (β1)/π₯ and Q = 2x Find integrating factor IF IF = e^β«1βπππ₯ IF = π^β«1βγ(β1)/π₯ ππ₯γ IF = π^(βlogβ‘π₯ ) IF = π^logβ‘γ(π₯)^(β1) γ IF = π^γlog γβ‘γ1/π₯γ IF = π/π Solution of the equation y Γ I.F = β«1βγπΈ Γ π°.π­.ππ+π γ Putting values, π¦ Γ1/π₯ = β«1βγ2π₯ Γ1/π₯ ππ₯γ+πΆ π¦/π₯ = β«1β2ππ₯+πΆ π¦/π₯ = 2π₯+πΆ π = ππ^π+πͺπ