Ex 9.5, 4 - Chapter 9 Class 12 Differential Equations
Last updated at April 16, 2024 by Teachoo
Solving Linear differential equations - Equation given
Ex 9.5, 19 (MCQ) Important
Misc 14 (MCQ) Important
Ex 9.5, 2
Ex 9.5, 10
Ex 9.5, 3 Important
Ex 9.5, 4 You are here
Misc 15 (MCQ)
Ex 9.5, 13
Ex 9.5, 8 Important
Misc 10 Important
Misc 11
Ex 9.5, 14 Important
Ex 9.5, 6
Ex 9.5, 5 Important
Ex 9.5, 9
Ex 9.5, 7 Important
Ex 9.5, 15
Example 14
Ex 9.5, 1 Important
Ex 9.5, 12 Important
Ex 9.5, 11
Example 16
Example 17 Important
Example 22 Important
Solving Linear differential equations - Equation given
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