
Ex 9.3
Last updated at Dec. 16, 2024 by Teachoo
Ex 9.3, 2 For each of the differential equations in Exercises 1 to 10, find the general solution : ๐๐ฆ/๐๐ฅ=โ(4โ๐ฆ^2 ) (โ2<๐ฆ<2) ๐๐ฆ/๐๐ฅ = โ(4โ๐ฆ2) ๐๐ฆ/โ(4 โ ๐ฆ^2 ) = dx. ๐ ๐/โ(๐^๐ โ ๐^๐ ) = dx Integrating both sides โซ1โใ๐๐ฆ/โ(2^2 โ ๐ฆ^2 )=โซ1โ๐๐ฅใ We know that โซ1โใ๐๐ฅ/โ(๐^2โ๐ฅ^2 )=sin^(โ1)โกใ๐ฅ/๐ใ ใ Putting ๐ = 2, x = y ใ๐๐๐ใ^(โ๐)โกใ๐/๐ใ = x + c ๐ฆ/2 = sin(x + c) y = 2 sin(x + c) โด y = 2 sin (x + c) is the general solution