Question

consider the equation y*dx+(x^2y-x)dy=0. show that the equation is not exact. find an integrating factor o the equation in the form u=u(x). find the general solution of the equation.

Answer #1

test if the equation ((x^4)(y^2) - y)dx + ((x^2)(y^4) - x)dy = 0 is
exact. If it is not exact, try to find an integrating factor. after
the equation is made exact, solve by looking for integrable
combinations

(1 point)
In this problem we consider an equation in differential form
Mdx+Ndy=0Mdx+Ndy=0.The equation
(4e−2y−(20x4y5e−x+2e−xsin(x)))dx+(−(20x5y4e−x+8e−2y))dy=0(4e−2y−(20x4y5e−x+2e−xsin(x)))dx+(−(20x5y4e−x+8e−2y))dy=0
in differential form M˜dx+N˜dy=0M~dx+N~dy=0 is not exact.
Indeed, we have
M˜y−N˜x=

3. Consider the equation (3x^2y + y^2)dx + (x^3 + 2xy + 5)dy =
0. (a) Verify this is an exact equation
(b) Solve the equation

Solve the following equation using integrating factor.
y dx + (2x − ye^y) dy = 0

Find the solution to the following equation using an appropriate
integrating factor.
Include largest interval solution is
valid for
x(dy/dx)-2y√(x)
=3√(x) y(1)= -1

engineering mathematics
solve
(3y2+2x+1)dx+(2xy+2y)dy=0
Find an integrating factor and solve the ode,tks.

Consider the differential equation y′′+ 9y′= 0.(
a) Let u=y′=dy/dt. Rewrite the differential equation as a
first-order differential equation in terms of the variables u.
Solve the first-order differential equation for u (using either
separation of variables or an integrating factor) and integrate u
to find y.
(b) Write out the auxiliary equation for the differential
equation and use the methods of Section 4.2/4.3 to find the general
solution.
(c) Find the solution to the initial value problem y′′+ 9y′=...

Consider the Bernoulli equation dy/dx + y = y^2, y(0) = −1
Perform the substitution that turns this equation into a linear
equation in the unknown u(x).
Solve the equation for u(x) using the Laplace transform.
Obtain the original solution y(x). Does it sound familiar?

Solve the Initial Value Problem:
a) dydx+2y=9, y(0)=0 y(x)=_______________
b) dydx+ycosx=5cosx,
y(0)=7d y(x)=______________
c) Find the general solution, y(t), which solves the problem
below, by the method of integrating factors.
8t dy/dt +y=t^3, t>0
Put the problem in standard form.
Then find the integrating factor, μ(t)= ,__________
and finally find y(t)= __________ . (use C as the unkown
constant.)
d) Solve the following initial value problem:
t dy/dt+6y=7t
with y(1)=2
Put the problem in standard form.
Then find the integrating...

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...

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