An ordinary differential equation (ODE) is an equation that involves derivatives, but no partial derivatives. The "dx" and "dy" found in the equation denote the derivatives involved. We read these notations as "with respect to x" (dx) and "with respect to y" (dy). Their inclusion in the equation makes it possible for us to solve using integration.

When solving an ODE, the simplest approach is to group together the x terms and the y terms so that we might integrate "with respect to x" and "with respect to y."

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(e^y + 1)^2 * e^-y dx + (e^x + 1) * e^-x dy = 0

An ordinary differential equation (ODE) is an equation that involves derivatives, but no partial derivatives. The "dx" and "dy" found in the equation denote the derivatives involved. We read these notations as "with respect to x" (dx) and "with respect to y" (dy). Their inclusion in the equation makes it possible for us to solve using integration.

When solving an ODE, the simplest approach is to group together the x terms and the y terms so that we might integrate "with respect to x" and "with ...

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In this example you will find a simple ordinary differential equation solved step-by-step with full work shown.

Sketch the direction fields for the following ODE's.
Make use of isoclines wherever possible.
a. y' = y - x + 1
b. y' = 2x
c. y' = y - 1
d. y' = xsquared + ysquared - 1
e. y' = y - xsquared
Please note y'=y prime. It looks diff, when i see the ?
#2.
In each direction field above sketch integral curves for which

(1) Use Laplace Transforms to solve Differential Equation
y'' - 8y' + 20 y = t (e^t) , given that y(0) = 0 , y'(0) = 0
(2) Use Laplace Transforms to solve Differential Equation
y''' + 2y'' - y' - 2y = Sin 3t , given that y(0)=0 , y'(0)=0 ,y''(0)=0, y'''(0)=1
Note: To see the questions in their mathematic

Hi,
Please help working on
section 1.1 problems 2,4,8,14,16
section 1.2 problems 6,10,20,24,27
thank you
See attached
Classify each as an ordinarydifferential equation (ODE) or a partial differential equation (PDE), give the order, and indicate the independent and dependent variables. If the equation is an ODE, ind

Consider the heat equation
delta(u)/delta(t) = (delta^2)(u)/delta(x^2)
Show that if u(c, t) = (t^alpha)psi(E) where E = x/sqrt(t) and alpha is a constant, then psi(E) satisfies the ordinarydifferential equation
alpha(psi) = 1/2 E(psi) = psi, where ' = d/dE
is independent of t only if alpha = - 1/2. Further, show th

Differential Equation (IX): Formation of DifferentialEquations by Elimination
Eliminate the arbitrary constants from the equation: y = Ae^x + Be^2x + Ce^3x. Make sure to show all of the steps which are involved.

Suppose m and k are positive numbers. Find u so that
mu''(t) + ku(t)= 0
for all numbers t and u(0)=1 and u'(0)=2.
(note: u'' = second derivative of u)
Please clarify any shorthand that you are using. Thanks!

I am asking for the step-by-step workings for all of the attached problems.
** Please see the attached file for complete problem description **
1st problems. Please find the general solution of:
(1) dy/dx = y/sin(y) - x
(2) dy/dx = y + cos(x)y^2010
In the process of finding the solutions for the problems make use of both