1. Chapter 9 Class 12 Differential Equations
2. Serial order wise

Transcript

Ex 9.3, 12 Which of the following differential equations has ๐ฆ=๐ฅ as one of its particular solution ? (A) (๐^2 ๐ฆ)/(๐๐ฅ^2 )โ๐ฅ^2 ๐๐ฆ/๐๐ฅ+๐ฅ๐ฆ=๐ฅ (B) (๐^2 ๐ฆ)/(๐๐ฅ^2 )+๐ฅ ๐๐ฆ/๐๐ฅ+๐ฅ๐ฆ=๐ฅ (C) ) (๐^2 ๐ฆ)/(๐๐ฅ^2 )โ๐ฅ^2 ๐๐ฆ/๐๐ฅ+๐ฅ๐ฆ=0 (D) (๐^2 ๐ฆ)/(๐๐ฅ^2 )+๐ฅ ๐๐ฆ/๐๐ฅ+๐ฅ๐ฆ=0 ๐ฆ=๐ฅ Differentiating both sides w.r.t. ๐ฅ ๐๐ฆ/๐๐ฅ=1 Again differentiating both sides w.r.t. ๐ฅ โด (๐^2 ๐ฆ)/(๐๐ฅ^2 )=0 Let us check each Options Option A (๐^2 ๐ฆ)/(๐๐ฅ^2 ) โ๐ฅ^2 ๐๐ฆ/๐๐ฅ +๐ฅ๐ฆ=๐ฅ 0โ๐ฅ^2 (1)+๐ฅ๐ฆ=๐ฅ โ๐ฅ^2+๐ฅ๐ฆ=๐ฅ โ๐ฅ^2+๐ฅ(๐ฅ)=๐ฅ โ๐ฅ^2+๐ฅ^2=๐ฅ 0=๐ฅ โด Option (A) is not possible Option B (๐^2 ๐ฆ)/(๐๐ฅ^2 ) +๐ฅ ๐๐ฆ/๐๐ฅ+๐ฅ๐ฆ=๐ฅ 0โ๐ฅ(1)+๐ฅ๐ฆ=๐ฅ ๐ฅ+๐ฅ๐ฆ=๐ฅ ๐ฅ๐ฆ=๐ฅโ๐ฅ ๐ฅ๐ฆ=๐ฅโ๐ฅ ๐ฅ(๐ฅ)=0 ๐ฅ^2=0 โด Option (B) is not possible Option C (๐^2 ๐ฆ)/(๐๐ฅ^2 )โ๐ฅ^2 ๐๐ฆ/๐๐ฅ+๐ฅ๐ฆ=0 0โ๐ฅ^2 (1)+๐ฅ๐ฆ=0 โ๐ฅ^2+๐ฅ๐ฆ=0 โ๐ฅ^2+๐ฅ(๐ฅ)=0 โ๐ฅ^2+๐ฅ^2=0 0=0 โด Option (C) is possible Option D (๐^2 ๐ฆ)/(๐๐ฅ^2 ) +๐ฅ ๐๐ฆ/๐๐ฅ+๐ฅ๐ฆ=0 0โ๐ฅ(1)+๐ฅ๐ฆ=0 ๐ฅ+๐ฅ๐ฆ=0 ๐ฅ+๐ฅ(๐ฅ)=0 ๐ฅ+๐ฅ^2=0 ๐ฅ^2=โ๐ฅ โด Option (C) is not possible โด Option c is correct