Differential Equation

50 answers

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

General Solution of Differential Equation Correct

Classify the following differential equation:

Both separable and linear Correct

Determine the order and degree of the differentialequation:

Fourth order, first degree Correct

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

-2cos2x Correct

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

5sin4x + c Correct

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

-4cos2x+c Correct

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

3 incorrect Correct

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

Integrating factor Correct

Integration is the reverse process of differentiation

True Correct

is a first orderpartial differential equation

True Correct

is a second order ordinary differential equation

False Correct

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

Ordinary Differential Equation Correct

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

Partial Differential Equation Correct

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

Differential Equations Correct

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

Particular Solution of Differential Equation Correct

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

Degree of Differential Equation Correct

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

4 incorrect Correct

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

True Correct

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

True Correct

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

True Correct

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

True Correct

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

True Correct

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

False Correct

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

True Correct

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

True Correct

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

False Correct

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

True Correct

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

False Correct

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

True Correct

The differential equationis

Linear Correct

The equation y2= cx is general solution of:

y’ = y / 2x Correct

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

y=(3/4)lnx-(1/3)x3+c incorrect Correct

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

lny=2sinx+c Correct

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

y=(1/4)sin4x-x2+c Correct

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

y=(1/2)+ce-x2 Correct

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

Acos2t + Bsin2t Correct

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

y=3+c/x Correct

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

xy2+y3=c Correct

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

True Correct

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

1 incorrect Correct

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

y=3x-(x2/2)-(1/2) Correct

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

True Correct

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

All of the above Correct

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

y=(x4/4) + 3(x2/2) + c Correct

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

05 incorrect Correct

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

False Correct

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

Linear Correct

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

False Correct

Which of the following equations is a variable separable DE?

2ydx = (x2+ 1)dy Correct

Which of the following equations is an exact DE?

2xy dx + (2 + x2)dy = 0 Correct