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# Differential Equation

A branch of mathematics that studies equations involving derivative, exploring their solutions and applications in various fields such as physics and economics.

## separable

In solving linear differential equations of the form dy/dx + Py = 0, the equationis called the

• Integrating factor

A solution to a differential equation which contains one or more arbitrary constants of integration is called:

• General Solution of Differential Equation

Integration is the reverse process of differentiation

• True

Which of the following equations is an exact DE?

• 2xy dx + (2 + x2)dy = 0

What is the order of the differential equation given bydy/dx+4y=sinx?

• 05 incorrect

The differential equationis

• Linear

The differential equation xydx-(x+2y)2dy=0 is a homogeneous differential equation

• True

The differential equation (x4+2y)dx-xdy=0 is a linear first order differential equation

• True

The equation y2= cx is general solution of:

• y’ = y / 2x

It is obtained when additional information is given so that constants may be calculated

• Particular Solution of Differential Equation

For the differential equation dy/dx = 4sin2x, what is the particular solution if y=2 when x=pi/2

• -2cos2x

is a second order ordinary differential equation

• False

is a first orderpartial differential equation

• True

The differential equation (x2-2xy)dx+4y2dy=0 is homogenous of degree 2

• True

Classify the following differential equation:

• Both separable and linear

It is a differential equation whose unknown function (dependent variable usually y) depends on only one independent variable

• Ordinary Differential Equation

The simplest form of partial differential equations occurs when a solution can be determined by direct partial integration

• True

Given the differential equationdy/dx=(x4−y4)/(x2+y2)xythe degree of differential equation is

• 3 incorrect

It is an equation involving an unknown function and its d (a)Polynomials derivatives

• Differential Equations

The general solution of the differential xdy/dx=3-y is

• y=3+c/x

The general solution of the differential equation 2x(dy/dx)=3-x3is

• y=(3/4)lnx-(1/3)x3+c incorrect

Determine the order and degree of the differentialequation:

• Fourth order, first degree

The differential equation x(dy/dx)=x-y is a linear differential equation of the degree 1

• True

When the right-hand side is not equal to zero it is referred to as ahomogeneous differential equation

• False

The differential equation (6x2-7y2)dx-14xydy=0 is homogeneous of degree 2

• True

When the right-hand side of the differential equation is zero, it is referred to asa non-homogeneous differential equation

• False

The differential equation xy2dy – (x3+y3)dx=0 is not a homogeneous differential equation

• False

Which of the following equations is a variable separable DE?

• 2ydx = (x2+ 1)dy

The differential equation t(dy/dt)-5t=-y is a linear differential equation of the degree 2

• False

The differential equation (x+6y)dx+xdy=0 is homogeneous of degree 1

• True

The differential equation (x2-3x2y)dx+8y2dy=0 is homogenous of degree 2

• False

The differential equation (x+7y)dx=-6xdy is homogeneous of degree 1

• True

The general solution of the differential equation T" + 4T = 0 is

• Acos2t + Bsin2t

The general solution of the differential equation dy/dx=2ycosx is

• lny=2sinx+c

What is the general solution for the differential equation dy/dx = x3+ 3x?

• y=(x4/4) + 3(x2/2) + c

It is the highest power of the highest differential which the equation contains after simplification

• Degree of Differential Equation

For the differential equation dy/dx = 6cos4x, what is the general solution?

• 5sin4x + c

To be able to solve simple partial differential equations which of the following knowledge is required?

• All of the above

The heat conduction equationis solved in a similar manner to that for the wave equation

• True

The differential equation dy/dx=(x4+5y)/x is a linear first order differential equation

• True

The order of the differential equation x4(d3y/dx3)+x(d2y/dx2) = 3 i

• 1 incorrect

It is a differential equation whose unknown function depends on two or more independent variables

• Partial Differential Equation

The differential equation (3x+2y)dx+2xdy=0 is homogeneous of degree 1

• True

For the differential equation dy/dx=8sin2x, what is the general solution?

• -4cos2x+c

The general solution of the differential equation dy/dx=x(1-2y) is

• y=(1/2)+ce-x2

When the right-hand side of the differential equation is zero, it is referred to asa homogeneous differential equation

• Linear

The general solution of the differential equation dy/dx=cos4x-2x is

• y=(1/4)sin4x-x2+c

The general solution of the homogeneous differential equation ydx+(2x+3y)dy=0 is

• xy2+y3=c

The particular solution of the differential equation (dy/dx)+x=3, given y=2, when x=1 is

• y=3x-(x2/2)-(1/2)

The degree of the differential equation x4(d3y/dx3)2+x(d2y/dx2)4= 3 is

• 4 incorrect
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