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30 March, 05:48

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

+2
Answers (1)
  1. 30 March, 09:13
    0
    (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
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Home » Mathematics » 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
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