Question

determine if the xy-plane for which the given differential equation would have a unique solution whose graph passes through the point (x0,y0) in the region

dy/dx=y^(2/3)

x(dy/dx)=y

Answer #1

Determine a region of the xy-plane for which the given
differential equation would have a unique solution whose graph
passes through a point (x_0, y_0) in the region. (1+y^3)y' =
x^2

1) Solve the given differential equation by using an appropriate
substitution. The DE is a Bernoulli equation.
x dy/dx +y= 1/y^2
2)Consider the following differential equation.
(25 − y2)y' = x2
Let f(x, y) = x^2/ 25-y^2. Find the derivative of f.
af//ay=
Determine a region of the xy-plane for which the given
differential equation would have a unique solution whose graph
passes through a point
(x0, y0) in the region.
a) A unique solution exists in the region consisting...

Consider the differential equation
y' =
y2 − 9
.
Let
f(x, y) =
y2 − 9
.
Find the partial derivative of f.
df
dy
=
Determine a region of the xy-plane for which the given
differential equation would have a unique solution whose graph
passes through a point
(x0, y0)
in the region.
A unique solution exits in the entire x y-plane.
A unique solution exists in the region −3 < y < 3.
A unique solution exits...

Determine all (?0, ?0 ) in the xy-plane for which the d.e. ??/??
= ?/? would have a unique solution whose graph passes through (?0,
?0 ).

dy/dx = ysin(4x)/(y-4)
a) Find region of xy plane where the d.e has a unique
solution
b) Solve the d.e by seperation of variables. Is there a lost
solution?
c) Find the solution of the ivp where the initial condition is
y(-pi) = -1

3. Find the general solution to the differential equation:
(x^2 + 1/( x + y) + y cos(xy)) dx + (y ^2 + 1 / (x + y) + x
cos(xy)) dy = 0

Find a particular solution to each of the following differential
equations with the given initial condition:
A) dy/dx=ysinx/1+y^2, y(0)=1
B)dy/dx=xy ln x, y(1)=3
C)xy(1+x^2) dy/dx=(1+y^2), y(1)=0

Find the general solution of the given differential equation
(x+!) dy/dx + (x+2)y = 2xe^-x
y = ______
Determine whether there are any transient terms in the general
solution.

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).

Find the General Solution of the Differential Equation (y' =
dy/dx) of
xy' = 6y+9x5*y2/3
I understand this is done with Bernoullis Equation but I can't seem
to algebraically understand this.

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