State the order of the given ordinary differential equations. Determine whether the equation is linear or nonlinear. 1. (1-x)y"-4xy'+5y=cosx
2. t^5 y^(4) - t^3 y" + 6y =0
3. (d^2Y/dx^2) = sqrt ((1+(dy/dx)^2))
4. (Sinθ)y"'- (cosθ)y' =2

In this exercise we have to use the knowledge of ordinary equations to determine the linear equations, in this way we find that:

1) Linear

2) Non Linear

3) Linear

4) Non linear

So from the knowledge in topics of ordinary equations we find that:

1)

2)

3)

4)

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(1-x)y"-4xy'+5y=cosx

= Second order

= linear

2. t^5 y^(4) - t^3 y" + 6y =0

= Second order

= non linear

3. (d^2Y/dx^2) = sqrt ((1+(dy/dx)^2))

= Second order

= Linear

4. (Sinθ)y"'- (cosθ)y' =2

= Third order

= Non linear

Step-by-step explanation:

(1-x)y"-4xy'+5y=cosx

= Second order

= linear

2. t^5 y^(4) - t^3 y" + 6y =0

= Second order

= non linear

3. (d^2Y/dx^2) = sqrt ((1+(dy/dx)^2))

= Second order

= Linear

4. (Sinθ)y"'- (cosθ)y' =2

= Third order

= Non linear

x^6

step-by-step explanation:

this is correct because:

x-6=0

0*x=0

so

x^6