Question

Homogenous Differential Equations:

dy/dx = y - 4x / x-y

dy/dx = - (4x +3y / 2x+y)

Answer #1

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differential equation(2x+3y)dx+ (y+2)dy=0

Solve the following system of differential equations:
dx/dt =x+2y
dy/dt =−x+3y

Homogeneous Differential Equations:
dy/dx = xy/x^(2) - y^(2)
dy/dx = x^2 + y^2 / 2xy

Solve the following differential equations.
a.) dy/dx+2xy=x, y(0)=2
b.) ?^2(dy/dx)−?y=−y^2

(* Problem 3 *)
(* Consider differential equations of the form a(x) + b(x)dy
/dx=0 *) \
(* Use mathematica to determin if they are in Exact form or not.
If they are, use CountourPlot to graph the different solution
curves 3.a 3x^2+y + (x+3y^2)dy /dx=0 3.b cos(x) + sin(x) dy /dx=0
3.c y e^xy+ x e^xydy/dx=0

Solve the first order homogeneous differential equation:
(2x-5y)dx + (4x-y) dy=0

Use the method for solving homogeneous equations to solve the
following differential equation.
(9x^2-y^2)dx+(xy-x^3y^-1)dy=0
solution is F(x,y)=C, Where C= ?

Consider the following system of differential equations dx/dt =
(x^2 + 2x + 1)(x^2 − 4x + 4) dy/dt = xy − 1
Which of the following is not an equilibrium point of the above
system? (A) (3, 1/3 ) (B) (−1, −1) (C) (1, 1) (D) (1, 3)

Use the method for solving equations of the form
dy/dx=G(ax+by)
to solve the following differential equation.
dy/dx=2sin(4x-2y) ignore lost solutions and give implicit
solution in the form F(x,y)=c

Use the Laplace transform to solve the given system of
differential equations. 2 dx/dt + dy/dt − 2x = 1
dx/dt + dy/dt − 6x − 6y = 2
x(0) = 0, y(0) = 0

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