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

Question

Mathematics

Tripp York

5 June, 07:17

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

+1

Answers (1)

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Nikhil Johnston · Answer 1

(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

State the order of the given ordinary differential equations. Determine whether the equation is linear or nonlinear.1. (1-x) y"-4xy'+5y=cosx2. t^5 y^ (4) - t^3 y" + 6y = 03. (d^2Y/dx^2) = sqrt ((1 + (dy/dx) ^2))4. (Sinθ) y"' - (cosθ) y' = 2

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