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