Question

1. Determine the order and the degree of the following differential equations: a. 5(frac{d^4x}{dy^4})^5 + 5(frac{dx}{dy})^{10} + x^7 - x^5 = 0 b. (y'')^2 + (y')^3 + 3y = x^2 c. y'' = [(y')^2 + 1]^{frac{3}{2}} d. (frac{d^2y}{dx^2})^{frac{3}{2}} - (frac{dy}{dx})^{frac{1}{2}} - 4 = 0 2. Solve the general solution of the given differential equations: a. xdx - y^2dy = 0 b. y' = frac{2xy}{x^2-y^2} c. (x + sin y)dx + (x cos y - 2y)dy = 0 d. y(4x + y)dx - 2(x^2 - y)dy = 0 e. (x^2 + y^2 + 1)dx + x(x - 2y)dy = 0

          1. Determine the order and the degree of the following differential equations:

a. 5(frac{d^4x}{dy^4})^5 + 5(frac{dx}{dy})^{10} + x^7 - x^5 = 0

b. (y'')^2 + (y')^3 + 3y = x^2

c. y'' = [(y')^2 + 1]^{frac{3}{2}}

d. (frac{d^2y}{dx^2})^{frac{3}{2}} - (frac{dy}{dx})^{frac{1}{2}} - 4 = 0

2. Solve the general solution of the given differential equations:

a. xdx - y^2dy = 0

b. y' = frac{2xy}{x^2-y^2}

c. (x + sin y)dx + (x cos y - 2y)dy = 0

d. y(4x + y)dx - 2(x^2 - y)dy = 0

e. (x^2 + y^2 + 1)dx + x(x - 2y)dy = 0

$1. Determine the order and the degree of the following differential equations: a. 5(fracd^4xdy^4)^5 + 5(fracdxdy)^10 + x^7 - x^5 = 0 b. (y”)^2 + (y')^3 + 3y = x^2 c. y” = [(y')^2 + 1]^frac32 d. (fracd^2ydx^2)^frac32 - (fracdydx)^frac12 - 4 = 0 2. Solve the general solution of the given differential equations: a. xdx - y^2dy = 0 b. y' = frac2xyx^2-y^2 c. (x + sin y)dx + (x cos y - 2y)dy = 0 d. y(4x + y)dx - 2(x^2 - y)dy = 0 e. (x^2 + y^2 + 1)dx + x(x - 2y)dy = 0$

Added by Laura W.

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