Differential Equation

MATH 6231 Differential Equation

What is the degree of the differential equation (dy/dx)2 – 3y(dy/dx) + xy =0?	2
Determine the order and degree of the differential equation:	Fourth order, first degree
The differential equation t(dy/dt)-5t=-y is a linear differential equation of the degree 2.	False
The general solution of the differential equation dy/dx=2ycosx is	lny=2sinx+c
The differential equation x(dy/dx)=x-y is a linear differential equation of the degree 1.	True
For the differential equation dy/dx = 4sin2x, what is the particular solution if y=2 when x=pi/2.	-2cos2x
It is the highest power of the highest differential which the equation contains after simplification.	Degree of Differential Equation
The differential equation (x+6y)dx+xdy=0 is homogeneous of degree 1.	True
The differential equation (x2-2xy)dx+4y2dy=0 is homogenous of degree 2.	True
The general solution of the differential equation dy/dx=cos4x-2x is	y=(1/4)sin4x-x2+c
The differential equation (x4 +2y)dx-xdy=0 is a linear first order differential equation.	True
The differential equation (x+7y)dx=-6xdy is homogeneous of degree 1.	True
What is the order of the differential equation dy/dx + y=x?	1
The order of the differential equation (d2r/dt2)3+(d2r/dt2)2+y(dr/dt)=0 is	2
The order of the differential equation:	2
Which of the following equations is a variable separable DE?	2ydx = (x2 + 1)dy
It is a differential equation whose unknown function depends on two or more independent variables.	Partial Differential Equation
What is the order of the differential equation (dy/dx)2 – 3y(dy/dx) + xy =0?	2
The order of the differential equation x4(d3y/dx3)+x(d2y/dx2) = 3 i	1 incorrect
The differential equation (3x+2y)dx+2xdy=0 is homogeneous of degree 1.	True
A solution to a differential equation which contains one or more arbitrary constants of integration is called:	General Solution of Differential Equation
The general solution of the differential equation 2x(dy/dx)=3-x3 is	y=(3/4)lnx-(1/3)x3+c incorrect
The degree of the differential equation (d2r/dt2)3+(d2r/dt2)2+y(dr/dt)=0 is	3
The differential equation xydx-(x+2y)2dy=0 is a homogeneous differential equation.	True
The equation y2 = cx is general solution of:	y’ = y / 2x
What is the order of the differential equation given by dy/dx+4y=sinx?	0.5 incorrect
Given the differential equation dy/dx=(x4−y4)/(x2+y2)xy the degree of differential equation is.	3 incorrect
The differential equation dy/dx=(x4 +5y)/x is a linear first order differential equation.	True
For the differential equation dy/dx = 6cos4x, what is the general solution?	1.5sin4x + c
The degree of the differential equation:	3
Classify the following differential equation:	Separable and not linear
The differential equation xy2dy – (x3+y3)dx=0 is not a homogeneous differential equation.	False
The general solution of the differential equation dy/dx=x(1-2y) is	y=(1/2)+ce-x2
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 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 (x2-3x2y)dx+8y2dy=0 is homogenous of degree 2.	False
What is the general solution for the differential equation dy/dx = x3 + 3x?	y=(x4/4) + 3(x2/2) + c
Which of the following equations is an exact DE?	2xy dx + (2 + x2)dy = 0
The general solution of the differential xdy/dx=3-y is	y=3+c/x
In solving linear differential equations of the form dy/dx + Py = 0, the equation is called the	Integrating factor
What is the degree of the differential equation dy/dx + y=x?	1
It is an equation involving an unknown function and its d (a)  Polynomials derivatives.	Differential Equations
It is obtained when additional information is given so that constants may be calculated.	Particular Solution of Differential Equation
The degree of the differential equation x4(d3y/dx3)2+x(d2y/dx2)4 = 3 is	4 incorrect
For the differential equation dy/dx=8sin2x, what is the general solution?	-4cos2x+c
The general solution of the homogeneous differential equation ydx+(2x+3y)dy=0 is	xy2+y3=c.
The differential equation (6x2-7y2)dx-14xydy=0 is homogeneous of degree 2.	True
Classify the following differential	Both separable and linear
Classify the following differential equation:	Linear and not separable
Classify the following differential equation:	Both separable and linear
The differential equation  is	Linear
When the right-hand side of the differential equation is zero, it is referred to as a non-homogeneous differential equation.	False
Integration is the reverse process of differentiation.	True
Given the differential equation dy/dx=(x4−y4)/(x2+y2)xy the degree of differential equation is.	1
It is obtained when additional information is given so that constants may be calculated.	Particular Solution of Differential Equation
The order of the differential equation:	2
The general solution of the homogeneous differential equation ydx+(2x+3y)dy=0 is	xy2+y3=c.
For the differential equation dy/dx=8sin2x, what is the general solution?	-4cos2x+c
Which of the following equations is a variable separable DE?	2ydx = (x2 + 1)dy
is a second order ordinary differential equation.	False
The heat conduction equation is solved in a similar manner to that for the wave equation.	True
The differential equation xy2dy – (x3+y3)dx=0 is not a homogeneous differential equation.	False
For the differential equation dy/dx = 6cos4x, what is the general solution?	1.5sin4x + c
The simplest form of partial differential equations occurs when a solution can be determined by direct partial integration	True
The differential equation (6x2-7y2)dx-14xydy=0 is homogeneous of degree 2.	True
The differential equation (x+7y)dx=-6xdy is homogeneous of degree 1.	True
The differential equation xydx-(x+2y)2dy=0 is a homogeneous differential equation.	True
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 (x+6y)dx+xdy=0 is homogeneous of degree 1.	True
When the right-hand side is not equal to zero it is referred to as a homogeneous differential equation.	False
In solving linear differential equations of the form dy/dx + Py = 0, the equation   is	Integrating factor
When the right-hand side of the differential equation is zero, it is referred to as a homogeneous differential equation.	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 by dy/dx+4y=sinx?	1
What is the order of the differential equation dy/dx + y=x?	1
The general solution of the differential equation  T" + 4T = 0 is	Acos2t + Bsin2t
The degree of the differential equation x4(d3y/dx3)2+x(d2y/dx2)4 = 3 is	3 incorrect
The differential equation t(dy/dt)-5t=-y is a linear differential equation of the degree 2.	False
To be able to solve simple partial differential equations which of the following knowledge is required?	All of the above
For the differential equation dy/dx = 4sin2x, what is the particular solution if y=2 when x=pi/2.	-2cos2x
The general solution of the differential equation dy/dx=2ycosx is	lny=2sinx+c
The general solution of the differential equation dy/dx=cos4x-2x is	y=(1/4)sin4x-x2+c
is a first order partial differential equation.	True
The general solution of the differential equation dy/dx=x(1-2y) is	y=(1/2)+ce-x2
The differential equation (3x+2y)dx+2xdy=0 is homogeneous of degree 1.	True
It is the highest power of the highest differential which the equation contains after simplification.	Degree of Differential Equation