Question

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.

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= ?

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

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

solve the differential equation...
(x2-1)(dy/dx)+xy=0

A Bernoulli differential equation is one of the form
dy/dx+P(x)y=Q(x)y^n (∗)
Observe that, if n=0 or 1, the Bernoulli equation is linear. For
other values of n, the substitution u=y^(1−n) transforms the
Bernoulli equation into the linear equation
du/dx+(1−n)P(x)u=(1−n)Q(x).
Consider the initial value problem xy′+y=−8xy^2, y(1)=−1.
(a) This differential equation can be written in the form (∗)
with P(x)=_____, Q(x)=_____, and n=_____.
(b) The substitution u=_____ will transform it into the linear
equation du/dx+______u=_____.
(c) Using the substitution in part...

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

(x-y)dx + (y+x)dy =0 Solve the differential equation

Solve the Differential Equation:
(2y^4 + xy)dx - (6x^2) dy= 0

1) Solve the given differential equation by separation of
variables.
exy
dy/dx = e−y +
e−6x −
y
2) Solve the given differential
equation by separation of variables.
y ln(x) dx/dy = (y+1/x)^2
3) Find an explicit solution of the given initial-value
problem.
dx/dt = 7(x2 + 1), x( π/4)= 1

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