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How do you explain the term 'exact differential equation'?

An exact differential equation is a type of first-order differential equation that can be expressed in the form ( M(x, y) , dx + N(x, y) , dy = 0 ), where ( M ) and ( N ) are continuously differentiable functions. An equation is considered exact if the partial derivative of ( M ) with respect to ( y ) equals the partial derivative of ( N ) with respect to ( x ), i.e., ( \frac{\partial M}{\partial y} = \frac{\partial N}{\partial x} ). This condition indicates that there exists a function ( \psi(x, y) ) such that ( d\psi = M , dx + N , dy ). Solving an exact differential equation involves finding this function ( \psi ).


What is the differential equation of y equals sin2x?

dy/dx = 2cos2x


What is the differential equation of the family of straight lines y equals mx?

dy/dx = m


Why x-3 equals 0 is non homogeneous?

Because homogeneous equations normally refer to differential equations. The one in the question is not a differential equation.


What are exact and inexact differentials?

Exact differentials refer to changes in a function that can be expressed as the total differential of that function, meaning there exists a scalar function whose differential equals the given expression. Inexact differentials, on the other hand, cannot be derived from a single function and typically arise in contexts like thermodynamics, where they represent changes in quantities that are path-dependent. In mathematical terms, an exact differential ( df ) satisfies the condition ( \frac{\partial^2 f}{\partial y \partial x} = \frac{\partial^2 f}{\partial x \partial y} ), while inexact differentials, such as ( dQ ) or ( dW ), do not meet this criterion.


What is the differential form of following equation ie square of volume plus square of pressure plus cube of temperature?

2VdV + 2PdP + 3T2dT (this is an expression, not an equation because there is no equals sign)


How do you solve first order partial differential equation y2p - xyq x(z-2y)?

The Answers community requires more information for this question. Please edit your question using words eg "plus", "divide", "equals" because the browser used for posting questions rejects most mathematical symbols.


The differential equation of the family of straight lines y equals mx is?

The differential equation of the family of straight lines y = mx is given by dy/dx = m. This equation represents that the slope of the line at any point is equal to the constant m. Different values of m will yield different lines within the family.


Can you solve the differential equation dy over dx equals y squared over e to the 2x power?

-2y square exp power -2x-1


A differential amplifier stage has collector resistors of 5.1k ohm each if ic1 equals 1.35ma and ic2 equals 1.29ma what is the differential output voltage?

If a differential amplifier stage has collector resistors of 5.1k ohms and if ic1 equals 1.35ma and ic2 equals 1.29ma the differential output voltage is 0.306 volts.(5.1 * 1.35) - (5.1 * 1.29)


How does one solve the differential equation y double prime plus y prime plus y equals zero?

Let y=ce^(rx). R^2+r+1=0. Quadratic equation to find R.


Is c equals ab to the second power a equation or expression?

It is an equation ... Anything with an equals is an equation 2+b=6 Anything without an equals is an expression 2+a