Check sibling questions

Ex 9.6, 10 - Find general solution: (x + y) dy/dx = 1 - Solving Linear differential equations - Equation given

Ex 9.6, 10 - Chapter 9 Class 12 Differential Equations - Part 2
Ex 9.6, 10 - Chapter 9 Class 12 Differential Equations - Part 3
Ex 9.6, 10 - Chapter 9 Class 12 Differential Equations - Part 4

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Transcript

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

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.