Question

Homogeneous Differential Equations:

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

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

Answer #1

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

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.

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

(2xy+x^2+3y^2)dy/dx+(y^2+2xy+3x^2)=0

solve the differential equation
(2y^2+2y+4x^2)dx+(2xy+x)dy=0

Consider the following differential equation: dy/dx =
−(3xy+y^2)/x^2+xy
(a) Rewrite this equation into the form M(x, y)dx + N(x, y)dy =
0. Determine if this equation is exact;
(b) Multiply x on both sides of the equation, is the new
equation exact?
(c) Solve the equation based on Part (a) and Part (b).

solve differential equation ((x)2 - xy +(y)2)dx - xydy
= 0
solve differential equation (x^2-xy+y^2)dx - xydy =
0

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