Ex 9.5, 4 - Chapter 9 Class 12 Differential Equations

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Ex 9.5, 4 - Find general solution: dy/dx + (sec x) y = tan x - Ex 9.5

part 2 - Ex 9.5, 4 - Ex 9.5 - Serial order wise - Chapter 9 Class 12 Differential Equations

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Transcript

Ex 9.5, 4 For each of the differential equation given in Exercises 1 to 12, find the general solution : ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ+(secโก๐‘ฅ )๐‘ฆ=๐‘ก๐‘Ž๐‘›๐‘ฅ(0โ‰ค๐‘ฅ<๐œ‹/2) Differential equation is of the form ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ + Py = Q where P = sec x and Q = tan x Finding integrating factor, IF = ๐‘’^โˆซ1โ–’ใ€–๐‘ ๐‘‘๐‘ฅใ€— IF = e^โˆซ1โ–’secโกใ€–๐‘ฅ ๐‘‘๐‘ฅใ€— IF = ใ€–e^๐‘™๐‘œ๐‘”ใ€—^|secโกใ€–๐‘ฅ + tanโก๐‘ฅ ใ€— | I.F = sec x + tan x Solution is y (IF) = โˆซ1โ–’(๐‘„ร—๐ผ.๐น) ๐‘‘๐‘ฅ+๐‘ y (sec x + tan x) = โˆซ1โ–’ใ€–๐ญ๐š๐งโก๐’™ (๐’”๐’†๐’„โก๐’™+๐ญ๐š๐งโกใ€–๐’™)ใ€— ใ€—+๐’„ y (sec x + tan x) = โˆซ1โ–’ใ€–tanโก๐‘ฅ secโก๐‘ฅ ใ€— ๐‘‘๐‘ฅ+โˆซ1โ–’ใ€–tan^2โก๐‘ฅ ๐‘‘๐‘ฅ+๐ถใ€— y (sec x + tan x) = sec x + โˆซ1โ–’ใ€–(sec^2โก๐‘ฅโˆ’1)ใ€— dx + c y (sec x + tan x) = sec x + ๐ญ๐š๐งโก๐’™ โˆ’ x + c

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