Ex 9.4, 9 - Chapter 9 Class 12 Differential Equations

Transcript

Ex 9.4, 9 For each of the differential equations in Exercises 1 to 10, find the general solution : = sin 1 = sin 1 = sin 1 dx Integrating both sides = sin 1 .1 y = sin 1 x 1 1 1 2 1. dx y = x 1 x 1 2 dx Let t = 1 x2 2xdx = dt x dx = 2 Hence, our equation becomes y = x sin 1 x 2 y = x sin 1 x + 2 y = x sin 1 x + 1 2 1 2 y = x sin 1 x + 1 2 1 2 + 1 1 2 + 1 + C y = x sin 1 x + 1 2 1 2 1 2 + y = x sin 1 x + + C Putting back value of t y = x sin 1 x + + C