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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.

differential equation

derivative

integral

linear

nonlinear

ordinary

partial

homogeneous

inhomogeneous

boundary value

initial value

solution

stability

equilibrium

exponential

separable

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

  • Ordinary Differential Equation

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

  • False

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

  • 3 incorrect

Classify the following differential equation:

  • Both separable and linear

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

  • Particular Solution of Differential Equation

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

  • True

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

  • True

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

  • y=3+c/x

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

  • 5sin4x + c

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

  • y=(3/4)lnx-(1/3)x3+c incorrect

is a second order ordinary differential equation

  • False

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

  • General Solution of Differential Equation

Which of the following equations is a variable separable DE?

  • 2ydx = (x2+ 1)dy

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

  • True

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

  • 1 incorrect

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

  • True

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

  • -2cos2x

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

  • True

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

  • False

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

  • All of the above

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

  • Acos2t + Bsin2t

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

  • Partial Differential Equation

is a first orderpartial differential equation

  • True

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

  • Integrating factor

Which of the following equations is an exact DE?

  • 2xy dx + (2 + x2)dy = 0

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

  • True

The equation y2= cx is general solution of:

  • y’ = y / 2x

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

Determine the order and degree of the differentialequation:

  • Fourth order, first degree

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

  • y=(1/2)+ce-x2

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

  • False

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

  • False

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

  • lny=2sinx+c

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

  • True

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

  • True

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

  • True

The differential equationis

  • Linear

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

  • xy2+y3=c

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

  • 4 incorrect

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

  • False

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

  • True

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

  • Degree of Differential Equation

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

  • y=(x4/4) + 3(x2/2) + c

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

  • True

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

  • Differential Equations

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

  • 05 incorrect

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

  • -4cos2x+c

Integration is the reverse process of differentiation

  • True
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