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Ex 9.6
Ex 9.6, 2
Ex 9.6, 3 Important
Ex 9.6, 4
Ex 9.6, 5 Important
Ex 9.6, 6
Ex 9.6, 7 Important
Ex 9.6, 8 Important
Ex 9.6, 9
Ex 9.6, 10 You are here
Ex 9.6, 11
Ex 9.6, 12 Important
Ex 9.6, 13
Ex 9.6, 14 Important
Ex 9.6, 15
Ex 9.6, 16 Important
Ex 9.6, 17 Important
Ex 9.6, 18 (MCQ)
Ex 9.6, 19 (MCQ) Important
Last updated at March 16, 2023 by Teachoo
Ex 9.6, 10 For each of the differential equation given in Exercises 1 to 12, find the general solution : ( + ) / =1 Step 1: Put in form / + Py = Q or / + P1x = Q1 (x + y) / = 1 Dividing by (x + y), / = 1/(( + )) / = ( + ) / x = / + ( 1) x = Step 2: Find P1 and Q1 Comparing (1) with / + P1x = Q1 P1 = 1 and Q1 = y Step 3: Find Integrating factor, I.F. I.F. = ^ 1 _1 = e^ 1 ( 1) = e y So, I.F. = e y Step 4 : Solution of the equation x I.F. = 1 1 . . + Putting values, x e y = 1 ^( ). + Let I = 1 . ^( ) = y 1 ^( ) 1 [ / 1 ^( ) ] dy = y ^( )/( 1) 1 1. ^( )/( 1) dy. = . ^( ) + 1 ^( ) = . ^( ) + ^( )/( 1) = . ^( ) ^( ) Putting value of I in (2) x e y = 1 ^( ). + x e y = ^( ) ^( )+ Dividing by ^( ) x = y 1 + Cey x + y + 1 = Cey