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