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. Consider the ODE dy/ dx = tanh(x) − y tanh(x). Use the
integrating factor method to find the general solution of the ODE.
Find the general solution of the ODE using a different method. Do
you get the same answer? Explain briefly.

(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=

Find an integrating factor and solve the O.D.E. 1 + (x/y −
sin(y) *dy/dx = 0.

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.

exact differential equation, (2xy+x)dx+(x^2+y)dy=0

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′=...

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