Question

Homogeneous Differential Equations:

dy/dx = xy/x^(2) - y^(2)

dy/dx = x^2 + y^2 / 2xy

Answer #1

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

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= ?

differential equations solve
(2xy+6x)dx+(x^2+4y^3)dy, y(0)=1

Solve the given differential equations:
a) dy/dx=(x+1)^2
b) (x+1)dy/dx-xy=x^2+x

exact differential equation, (2xy+x)dx+(x^2+y)dy=0

Solve the Homogeneous differential equation
(7 y^2 + 1 xy)dx - 1 x^2 dy = 0
(a) A one-parameter family of solution of the equation is y(x)
=
(b) The particular solution of the equation subject to the
initial condition y(1) =1/7.

Find general solution to the equations:
1)y'=x-1-y²+xy²
2)xy²dy=(x³+y³)dx

Homogenous Differential Equations:
dy/dx = y - 4x / x-y
dy/dx = - (4x +3y / 2x+y)

(61). (Bernoulli’s Equation): Find the general solution of the
following first-order differential equations:(a) x(dy/dx)+y=
y^2+ln(x) (b) (1/y^2)(dy/dx)+(1/xy)=1

(* 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

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