Question

can i have a step by step of 1, 3, and 5 please

In Problems 1-6, determine whether the given equation is separable, linear, neither or both. dx 1. +xt = ex 2. 2dy +sin x y = 0 dt dx 3. 3t e'+ y ln t 4. (t+ \ dt yt - y dy Srortar dr 5. 3r = de vorla (d) dx TU6. x +Px = sin t dt 03

Answer 1

An ordinary differential equ^n of the from dy/dx + P (x) y = Q (x) is a linear differential equ^n of first order in y 1. Here the given diff equ^n is dx/dt + xt = e^x - - (i) This is not a linear differential equation since e^x is not a function of the independent variable t Also the function of x and t can not be separate Therefore the given equ^n (i) is not seperable Thus the given equ^n (i) is neither linear nor seperable. The given equ^n is 3t = e^t dy/dt + y ln t or, e^t dy/dt + y ln t = 3t or, dy/dt + (ln t/e^t) y = 3t/e^t - - (i) Since ln t/e^t and 3t/e^t are functions of the independent variable t hence the given differential equ^n is a linear differential equ^n of first order in y But the differential equ^n is not