Question

Classification of DE's If a differential equation can be written as a linear combination of the unknown function and its derivatives, it is called linear. Note that the coefficients may be functions of the independent function. Here is the most general form of a linear ODE of order n: a0(t)y^(n) + a1(t)y^(n-1) + ... + an(t)y = g(t) Otherwise, the DE is called nonlinear. Example 5. Classify each DE as an ordinary or partial, linear or nonlinear, and indicate its order. a) (x^2y'' + y) / y' = cos x b) y'' + (y^2 - 1)y' - t^3y = tan t c) u_xxx - 3u_xy + (x^2 + y^3)u_x = 1 + u d) u_xx + uu_y = 0

          Classification of DE's
If a differential equation can be written as a linear combination of the unknown function and its derivatives, it is called linear. Note that the coefficients may be functions of the independent function.
Here is the most general form of a linear ODE of order n:
a0(t)y^(n) + a1(t)y^(n-1) + ... + an(t)y = g(t)
Otherwise, the DE is called nonlinear.
Example 5. Classify each DE as an ordinary or partial, linear or nonlinear, and indicate its order.
a) (x^2y'' + y) / y' = cos x
b) y'' + (y^2 - 1)y' - t^3y = tan t
c) u_xxx - 3u_xy + (x^2 + y^3)u_x = 1 + u
d) u_xx + uu_y = 0

Classification of DE's
If a differential equation can be written as a linear combination of the unknown function and its derivatives, it is called linear. Note that the coefficients may be functions of the independent function.
Here is the most general form of a linear ODE of order n:
a0(t)y^(n) + a1(t)y^(n-1) + ... + an(t)y = g(t)
Otherwise, the DE is called nonlinear.
Example 5. Classify each DE as an ordinary or partial, linear or nonlinear, and indicate its order.
a) (x^2y” + y) / y' = cos x
b) y” + (y^2 - 1)y' - t^3y = tan t
c) uxxx - 3uxy + (x^2 + y^3)ux = 1 + u
d) uxx + uuy = 0

Added by Joseph M.

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