Ex 9.4, 10 - Chapter 9 Class 12 Differential Equations

Transcript

Ex 9.4, 10 For each of the differential equations in Exercises 1 to 10, find the general solution : ^ tan +(1 ^ ) sec^2 =0 ^ tan +(1 ^ ) sec^2 =0 ^ tan = (1 ^ ) sec^2 ^ tan =( ^ 1) sec^2 ^ /( ^ 1) dx = ( 2 )/tan Integrating both sides. 1 ^ /( ^ 1) = 1 ( 2 )/tan Put ^ 1 = u and put tan y = v Diff u w.r.t. x & v w.r.t y Therefore 1 / / = 1 2 /( 2 ) dv 1 / = 1 / log u + c1 = log v Putting back u = ex 1 and V = tan y log |"ex 1" | + c1 = log tan y Putting c1 = log c log |"ex 1" |+ log c = log (tan y) log | ("ex 1" )|= log |tan | ("ex 1" ) = tan y tan y = c ("ex 1" ) is the general solution