Question

(1 point) Given the following differential equation

(x2+2y2)dxdy=1xy,

(a) The coefficient functions are M(x,y)= and N(x,y)= (Please input
values for both boxes.)

(b) The separable equation, using a substitution of y=ux, is

dx+ du=0 (Separate the variables with x with dx only and u with du
only.) (Please input values for both boxes.)

(c) The solution, given that y(1)=3, is

x=

**Note:** *You can earn partial credit on this
problem.*

I just need part C. thank you

Answer #1

(1 point) Given the following initial value problem
(x2+2y2)dxdy=xy,y(−3)=3
find the following:
(a) The coefficient functions are M(x,y)= and N(x,y)= . (Please
input values for both boxes.)
(b) The separable equation using a substitution of y=ux, is
dx+ du=0 (Separate the variables with x with dx only and u with du
only.) (Please input values for both boxes.)
(c) The implicit solution is
x=
I just need part C.

A Bernoulli differential equation is one of the form
dxdy+P(x)y=Q(x)yn
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)
Use an appropriate substitution to solve the equation
y'−(3/x)y=y^4/x^2 and find the solution that satisfies y(1)=1

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 (∗)
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(b) The substitution u=_____ will transform it into the linear
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(c) Using the substitution in part...

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t, write an eigenvalue problem in terms of X(x) that the equation
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exy
dy/dx = e−y +
e−6x −
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2) Solve the given differential
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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

(1 point) A Bernoulli differential equation is one of the
form
dydx+P(x)y=Q(x)yn (∗)
Observe that, if n=0 or 1, the Bernoulli equation is linear. For
other values of n, the substitution u=y1−n transforms the Bernoulli
equation into the linear equation
dudx+(1−n)P(x)u=(1−n)Q(x).dudx+(1−n)P(x)u=(1−n)Q(x).
Consider the initial value problem
y′=−y(1+9xy3), y(0)=−3.
(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
dudx+ u= .
(c) Using...

(a) Separate the following partial differential equation into
two ordinary differential equations: e 5t t 6 Uxx + 7t 2 Uxt − 6t 2
Ut = 0. (b) Given the boundary values Ux (0,t) = 0 and U(2π,t) = 0,
for all t, write an eigenvalue problem in terms of X(x) that the
equation in (a) must satisfy. That is, state (ONLY) the resulting
eigenvalue problem that you would need to solve next. You do not
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In each case, after your work is complete say whether the
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a. y= -x-1
b. y= e^x -x
c. y=2e^x-x-1

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−(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).

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...

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