Ex 9.6, 10 - Chapter 9 Class 12 Differential Equations (Term 2)

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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