Differential Equations Answers

A)Solve the following simultaneous inequalities
8x - 3≤ 1/4 [x + 16]< x + 10

B) Differentiate the following functions
y = x^3+〖6x〗^(-4)-〖4x〗^(1/2)+ 10

y = (〖6x〗^3+〖4x〗^2+3)(〖2x〗^2-〖4x〗^(-2)+5)

Solve 2 dy/dx+y tan⁡x = (4x+5)^2/cos⁡x y^3

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y'''+y''=8x^2 metodo anulador

10 One of the following is not a sufficient conditions for the existence of solution of the first order equation dy/dx = f(x,y), with y(x0)=y0
in a region T defined by |x−x0|<a and |y−y0


i. f is continuous in T

II. f is bounded in T

III. ∂f/∂y is continuous in T

IV. ∂f/∂y is not continuous in T

8 One of these is a homogeneous equation

I. h(x,y)=x^3+2xy+3xy^2+4y^3

II. h(x,y)=x^2+2x^2y+3xy^2+4y^3

III. h(x,y)=x^3+2x^2y+3xy^2+4y^3

IV. h(x,y)=x^3+2xy+3xy^2+4y^2
9 One of the following is not a separable equation

i. dy/dx=e^x+y

II. dy/dx=e^xy

III. dy/dx=x^2(y+y^2)

IV. (1+y^2)dx+(1+x^3)dy