Determine if the equation is linear or non-linear and indicate

William Collins

William Collins

Answered question

2022-01-19

Determine if the equation is linear or non-linear and indicate the order of the differential equation and would you tell me why please
(2x3+y)dxxdy=0
ydx(x+6y2)dy=0
(x+y)dx+tan(x)dy=0
6xydx+(4y+9x2)dy=0

Answer & Explanation

Karen Robbins

Karen Robbins

Beginner2022-01-19Added 49 answers

We have to tell the order of the following differential equations:
1.dydx=2x3+yx
2.dydx=yx+6y2
3.dydx=x+ytan(x)
Part 1
It is a first order differential equation. We can write it as below:
dydx=2x3+yx
dydx=2x2+yx
dydx1xy=2x2
It has the form of the linear differential equation dydx+Py=Q where
P and Q are functions of x only.
Therefore, it is a linear differential equation.
Part 2
It is a first order differential equation. We can write it as below:
dydx=yx+6y2
dxdy=x+6y2y
dxdy=1yx+6y
dxdy1yx=6y
It has the form of the linear differential equation dxdy+Rx=S where
R and S are functions of y only.
Therefore, it is a linear differential equation.
Part 3
It is a first order differential equation. We can write it as below:
dydx=x+ytan(x)
yx=xtan(x)1tan(y)y
dydx+1tan(x)y=xtan(x)
It has the form of the linear differential equation

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