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A branch of mathematics that studies equations involving derivative, exploring their solutions and applications in various fields such as physics and economics.
The differential equationis
To be able to solve simple partial differential equations which of the following knowledge is required?
The differential equation x(dy/dx)=x-y is a linear differential equation of the degree 1
It is an equation involving an unknown function and its d (a)Polynomials derivatives
The simplest form of partial differential equations occurs when a solution can be determined by direct partial integration
The differential equation (x2-2xy)dx+4y2dy=0 is homogenous of degree 2
The differential equation t(dy/dt)-5t=-y is a linear differential equation of the degree 2
The general solution of the homogeneous differential equation ydx+(2x+3y)dy=0 is
The differential equation (x+6y)dx+xdy=0 is homogeneous of degree 1
For the differential equation dy/dx = 4sin2x, what is the particular solution if y=2 when x=pi/2
It is a differential equation whose unknown function (dependent variable usually y) depends on only one independent variable
The general solution of the differential equation dy/dx=cos4x-2x is
The differential equation dy/dx=(x4+5y)/x is a linear first order differential equation
A solution to a differential equation which contains one or more arbitrary constants of integration is called:
The general solution of the differential equation 2x(dy/dx)=3-x3is
The particular solution of the differential equation (dy/dx)+x=3, given y=2, when x=1 is
The equation y2= cx is general solution of:
The heat conduction equationis solved in a similar manner to that for the wave equation
Given the differential equationdy/dx=(x4−y4)/(x2+y2)xythe degree of differential equation is
When the right-hand side is not equal to zero it is referred to as ahomogeneous differential equation
The differential equation xydx-(x+2y)2dy=0 is a homogeneous differential equation
The differential equation xy2dy – (x3+y3)dx=0 is not a homogeneous differential equation
When the right-hand side of the differential equation is zero, it is referred to asa non-homogeneous differential equation
Classify the following differential equation:
The differential equation (x4+2y)dx-xdy=0 is a linear first order differential equation
Determine the order and degree of the differentialequation:
When the right-hand side of the differential equation is zero, it is referred to asa homogeneous differential equation
In solving linear differential equations of the form dy/dx + Py = 0, the equationis called the
Integration is the reverse process of differentiation
The general solution of the differential equation T" + 4T = 0 is
For the differential equation dy/dx = 6cos4x, what is the general solution?
The differential equation (6x2-7y2)dx-14xydy=0 is homogeneous of degree 2
Which of the following equations is an exact DE?
It is obtained when additional information is given so that constants may be calculated
The differential equation (x2-3x2y)dx+8y2dy=0 is homogenous of degree 2
The order of the differential equation x4(d3y/dx3)+x(d2y/dx2) = 3 i
What is the general solution for the differential equation dy/dx = x3+ 3x?
It is a differential equation whose unknown function depends on two or more independent variables
is a first orderpartial differential equation
It is the highest power of the highest differential which the equation contains after simplification
Which of the following equations is a variable separable DE?
The differential equation (3x+2y)dx+2xdy=0 is homogeneous of degree 1
The degree of the differential equation x4(d3y/dx3)2+x(d2y/dx2)4= 3 is
The general solution of the differential xdy/dx=3-y is
For the differential equation dy/dx=8sin2x, what is the general solution?
The general solution of the differential equation dy/dx=2ycosx is
The general solution of the differential equation dy/dx=x(1-2y) is
is a second order ordinary differential equation
What is the order of the differential equation given bydy/dx+4y=sinx?
The differential equation (x+7y)dx=-6xdy is homogeneous of degree 1
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