



Subscribe to our Youtube Channel - https://you.tube/teachoo
Last updated at Dec. 10, 2019 by Teachoo
Transcript
Ex 9.3, 12 Which of the following differential equations has ๐ฆ=๐ฅ as one of its particular solution ? (A) (๐^2 ๐ฆ)/(๐๐ฅ^2 )โ๐ฅ^2 ๐๐ฆ/๐๐ฅ+๐ฅ๐ฆ=๐ฅ (B) (๐^2 ๐ฆ)/(๐๐ฅ^2 )+๐ฅ ๐๐ฆ/๐๐ฅ+๐ฅ๐ฆ=๐ฅ (C) ) (๐^2 ๐ฆ)/(๐๐ฅ^2 )โ๐ฅ^2 ๐๐ฆ/๐๐ฅ+๐ฅ๐ฆ=0 (D) (๐^2 ๐ฆ)/(๐๐ฅ^2 )+๐ฅ ๐๐ฆ/๐๐ฅ+๐ฅ๐ฆ=0 ๐ฆ=๐ฅ Differentiating both sides w.r.t. ๐ฅ ๐๐ฆ/๐๐ฅ=1 Again differentiating both sides w.r.t. ๐ฅ (๐^2 ๐ฆ)/(๐๐ฅ^2 )=0 Let us check each Options Option A (๐^2 ๐ฆ)/(๐๐ฅ^2 ) โ๐ฅ^2 ๐๐ฆ/๐๐ฅ +๐ฅ๐ฆ=๐ฅ Putting (๐^2 ๐ฆ)/(๐๐ฅ^2 ) = 1, ๐๐ฆ/๐๐ฅ = 0, y = x 0โ๐ฅ^2 (1)+๐ฅ(๐ฅ)=๐ฅ โ๐ฅ^2+๐ฅ^2=๐ฅ 0=๐ฅ Since this is not true โด Option (A) is not possible Option B (๐^2 ๐ฆ)/(๐๐ฅ^2 ) +๐ฅ ๐๐ฆ/๐๐ฅ+๐ฅ๐ฆ=๐ฅ Putting (๐^2 ๐ฆ)/(๐๐ฅ^2 ) = 1, ๐๐ฆ/๐๐ฅ = 0, y = x 0+๐ฅ(1)+๐ฅ(๐ฅ)=๐ฅ ๐ฅ+๐ฅ^2=๐ฅ ๐ฅ^2=0 Since this is not true โด Option (B) is not possible Option C (๐^2 ๐ฆ)/(๐๐ฅ^2 )โ๐ฅ^2 ๐๐ฆ/๐๐ฅ+๐ฅ๐ฆ=0 Putting (๐^2 ๐ฆ)/(๐๐ฅ^2 ) = 1, ๐๐ฆ/๐๐ฅ = 0, y = x 0โ๐ฅ^2 (1)+๐ฅ(๐ฅ)=0 โ๐ฅ^2+๐ฅ^2=0 0=0 Since this is true โด Option (C) is possible Option D (๐^2 ๐ฆ)/(๐๐ฅ^2 ) +๐ฅ ๐๐ฆ/๐๐ฅ+๐ฅ๐ฆ=0 Putting (๐^2 ๐ฆ)/(๐๐ฅ^2 ) = 1, ๐๐ฆ/๐๐ฅ = 0, y = x 0+๐ฅ(1)+๐ฅ(๐ฅ)=0 ๐ฅ+๐ฅ^2=0 ๐ฅ=โ๐ฅ^2 Since this is not true โด Option (D) is not possible Thus, Option C is correct
Ex 9.3
Ex 9.3, 2 Not in Syllabus - CBSE Exams 2021
Ex 9.3, 3 Important Not in Syllabus - CBSE Exams 2021
Ex 9.3, 4 Not in Syllabus - CBSE Exams 2021
Ex 9.3, 5 Important Not in Syllabus - CBSE Exams 2021
Ex 9.3, 6 Not in Syllabus - CBSE Exams 2021
Ex 9.3, 7 Important Not in Syllabus - CBSE Exams 2021
Ex 9.3, 8 Not in Syllabus - CBSE Exams 2021
Ex 9.3, 9 Not in Syllabus - CBSE Exams 2021
Ex 9.3, 10 Important Not in Syllabus - CBSE Exams 2021
Ex 9.3, 11 Not in Syllabus - CBSE Exams 2021
Ex 9.3, 12 Not in Syllabus - CBSE Exams 2021 You are here
About the Author