Classify the DEs in terms of Number of Variables Order Linea

Classify the DEs in terms of Number of Variables, Order, Linearity, Homogeneity, Type of Coefficients, and Number of Boundary Conditions Needed. And if it is a PDE, specify also the Type(and Region) of the PDE. (y\')^3 + 2y\" - x^2y + 4 = 0 m_1x_1\" + (k_1 + k_12)x_1 - k_12x_2 = f_1(t) m_2x_2\" - k_12x_1 + (k_2 + k_12)X_2 = f_2(t) (1 - y) Phi_xx + 2(1 - x) Phi_xy + (1 + y) Phi_yy = 0

Solution

1. order of differential equation ----- 2 beacuse th highest differential is second derivative of y - y\'\'

number of variables -- 1 ------- x

linearity -- non linear beause y\' has a 3rd power

homogeniety - it is not homogenous as power of y\'\' is 1 and power of x^2y is combined 3

type of coefficients - numbers as the constants are numbers.

number of boundary conditions required --- 2

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2. order of differential equation ----- 2 beacuse th highest differential is second derivative of x1 and x2 - y\'\'

number of variables -- 1 ------- 1

linearity -- linear beause y\' has a power 1

homogeniety - homogenous as power of y\'\' is 1 and power of x^2y is combined 3

type of coefficients - are matrices instead of numbers

number of boundary conditions required --- 2

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3-

. order of differential equation ----- 2 beacuse th highest differential is second derivative of x1 and x2 - y\'\'

number of variables -- 1 ------- 2

linearity -- non linear beause y\' has a power 2

homogeniety - homogenous as power of y\'\' is 2 and power of terms is combined 2 for all

type of coefficients - numbers

number of boundary conditions required --- 2