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 (∗)
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...

(a) Separate the following partial differential equation into
two ordinary differential equations: Utt + 4Utx − 2U = 0. (b) Given
the boundary values U(0,t) = 0 and Ux (L,t) = 0, L > 0, for all
t, write an eigenvalue problem in terms of X(x) that the equation
in (a) must satisfy.

(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
need to actually solve...

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

Check if the following functions satisfy the differential
equation dy/dx = x+y.
In each case, after your work is complete say whether the
function fits the equation.
a. y= -x-1
b. y= e^x -x
c. y=2e^x-x-1

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).

The indicated function y1(x) is a solution of the
given differential equation. Use reduction of order, to find a
second solution dx **Please do not solve this via the
formula--please use the REDUCTION METHOD ONLY.
y2(x)= ??
Given: y'' + 2y' + y = 0; y1 =
xe−x

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