Verify that ax 2 + by 2 = 1 is a solution of the differential equation x(yy 2 + y 1 2 ) = yy 1
This is a question of CBSE Sample Paper - Class 12 - 2017/18.
You can download the question paper here https://www.teachoo.com/cbse/sample-papers/


Last updated at Sept. 14, 2018 by Teachoo
This is a question of CBSE Sample Paper - Class 12 - 2017/18.
You can download the question paper here https://www.teachoo.com/cbse/sample-papers/
Transcript
Question 10 Verify that ax2 + by2 = 1 is a solution of the differential equation x(yy2 + y12) = yy1 Given ax2 + by2 = 1 First we find y1, and y2 Now, ax2 + by2 = 1 Differentiating w.r.t. x (ax2)โ+ (by2)โ = (1)โ 2ax + 2by ๐๐ฆ/๐๐ฅ = 0 2ax + 2byy1 = 0 2(ax + byy1) = 0 ax + byy1 = 0 Now, finding y2 From (1) ax + byy1 = 0 ax + by๐๐ฆ/๐๐ฅ = 0 Differentiating w.r.t. x (ax)โ + ("by" ๐๐ฆ/๐๐ฅ)^โฒ= 0 a + b("y" ๐๐ฆ/๐๐ฅ)^โฒ= 0 a + b(๐ฆ^โฒ ๐๐ฆ/๐๐ฅ+๐ฆ๐ฆโฒโฒ)= 0 a + b(๐ฆ^โฒ ๐ฆโฒ+๐ฆ๐ฆโฒโฒ)= 0 a + b(๐ฆ1 ๐ฆ1+๐ฆ๐ฆ2)= 0 a + b(๐ฆ1 ๐ฆ1+๐ฆ๐ฆ2)= 0 a + b(ใ๐ฆ_1ใ^2+๐ฆ๐ฆ2)= 0 a = โ b(ใ๐ฆ_1ใ^2+๐ฆ๐ฆ2) Now, from (1) ax + byy1 = 0 Putting a = โ b(ใ๐ฆ_1ใ^2+๐ฆ๐ฆ2) from (2) โ b(ใ๐ฆ_1ใ^2+๐ฆ๐ฆ2)x + byy1 = 0 byy1 = b(ใ๐ฆ_1ใ^2+๐ฆ๐ฆ2)x Cancelling b both sides yy1 = (ใ๐ฆ_1ใ^2+๐ฆ๐ฆ2)x x(ใ๐ฆ_1ใ^2+๐ฆ๐ฆ2) = yy1 Hence proved
CBSE Class 12 Sample Paper for 2018 Boards
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
Question 10 You are here
Question 11
Question 12
Question 13
Question 14
Question 15
Question 16
Question 17
Question 18
Question 19
Question 20
Question 21
Question 22
Question 23
Question 24
Question 25
Question 26
Question 27
Question 28
Question 29
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