11-28-2014, 09:31 PM
An equation is a 1st order linear equation if it can be written as dy / dx + p(x)y = q(x).
(i). x dy / dx + y = 2x.
There is no function p(x) in the above equation hence it is non linear.
(ii). xy dy / dx + (x^2)(y^2) = 2.
Here y is raise to the power 2, for linear eq y has to be power of 1. hence it is also on linear.
(iii). dy / dx + 3(x^2)y = 6x^2.
it can be written as dy / dx + p(x)y = q(x).
This equation is linear.
(iv). cos^3x dy / dx + ycosx = sinx
it can be written as dy / dx + p(x)y = q(x).
It is linear.
(v). x^2dy + y^2x = 0
I thinks its non linear.
Errors and omissions are excepted.
(i). x dy / dx + y = 2x.
There is no function p(x) in the above equation hence it is non linear.
(ii). xy dy / dx + (x^2)(y^2) = 2.
Here y is raise to the power 2, for linear eq y has to be power of 1. hence it is also on linear.
(iii). dy / dx + 3(x^2)y = 6x^2.
it can be written as dy / dx + p(x)y = q(x).
This equation is linear.
(iv). cos^3x dy / dx + ycosx = sinx
it can be written as dy / dx + p(x)y = q(x).
It is linear.
(v). x^2dy + y^2x = 0
I thinks its non linear.
Errors and omissions are excepted.