# Ex 9.5, 4 - Chapter 9 Class 12 Differential Equations

Last updated at April 16, 2024 by Teachoo

Ex 9.5

Ex 9.5, 1
Important

Ex 9.5, 2

Ex 9.5, 3 Important

Ex 9.5, 4 You are here

Ex 9.5, 5 Important

Ex 9.5, 6

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Ex 9.5, 8 Important

Ex 9.5, 9

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Ex 9.5, 12 Important

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Ex 9.5, 16 Important

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Ex 9.5, 18 (MCQ)

Ex 9.5, 19 (MCQ) Important

Last updated at April 16, 2024 by Teachoo

Ex 9.5, 4 For each of the differential equation given in Exercises 1 to 12, find the general solution : ๐๐ฆ/๐๐ฅ+(secโก๐ฅ )๐ฆ=๐ก๐๐๐ฅ(0โค๐ฅ<๐/2) Differential equation is of the form ๐๐ฆ/๐๐ฅ + Py = Q where P = sec x and Q = tan x Finding integrating factor, IF = ๐^โซ1โใ๐ ๐๐ฅใ IF = e^โซ1โsecโกใ๐ฅ ๐๐ฅใ IF = ใe^๐๐๐ใ^|secโกใ๐ฅ + tanโก๐ฅ ใ | I.F = sec x + tan x Solution is y (IF) = โซ1โ(๐ร๐ผ.๐น) ๐๐ฅ+๐ y (sec x + tan x) = โซ1โใ๐ญ๐๐งโก๐ (๐๐๐โก๐+๐ญ๐๐งโกใ๐)ใ ใ+๐ y (sec x + tan x) = โซ1โใtanโก๐ฅ secโก๐ฅ ใ ๐๐ฅ+โซ1โใtan^2โก๐ฅ ๐๐ฅ+๐ถใ y (sec x + tan x) = sec x + โซ1โใ(sec^2โก๐ฅโ1)ใ dx + c y (sec x + tan x) = sec x + ๐ญ๐๐งโก๐ โ x + c