Ex 9.6, 1 - Chapter 9 Class 12 Differential Equations

Transcript

Ex 9.6, 1 For each of the differential equation given in Exercises 1 to 12, find the general solution : +2 = Step 3: Find integrating factor, I.F. I.F. = e I.F. = 2 = 2 So, I.F = 2 Step 4 : Solution of the equation y I.F = . . + Putting values, 2 = sin . . 2 . + = sin . 2 . = sin x 2 . sin 2 = sin x 2 cos 2 2 dx = 1 2 sin 2 1 2 cos 2 cos 2 dx = 1 2 sin 2 1 2 cos 2 2 ( sin x) 2 2 = 1 2 sin 2 1 2 cos 2 2 + 1 2 = 1 2 sin 2 1 2 cos 2 2 + 1 2 + C I = 1 2 sin x 2 1 4 cos x 2 1 4 I + C I + 1 4 I = 1 4 2 sin 2 cos 2 + C 5 4 = 2 4 2 sin cos + C = 2 5 2 sin cos + C Now, Putting value of I in (2) y 2 = 2 5 2 sin cos + C y = +