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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.

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

**Differential Equations**

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

**False**

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

**Ordinary Differential Equation**

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

**True**

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

**True**

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

**True**

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

**lny=2sinx+c**

The differential equationis

**Linear**

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

**True**

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

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

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

**xy2+y3=c**

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

**True**

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

**True**

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

**All of the above**

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

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

is a second order ordinary differential equation

**False**

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

**True**

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

**y=3+c/x**

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

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

Which of the following equations is an exact DE?

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

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

**Acos2t + Bsin2t**

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

**Partial Differential Equation**

is a first orderpartial differential equation

**True**

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

**True**

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

**Integrating factor**

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

**4 incorrect**

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

**True**

Integration is the reverse process of differentiation

**True**

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

**Linear**

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

**False**

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 2x(dy/dx)=3-x3is

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

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

**-4cos2x+c**

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

**3 incorrect**

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

**General Solution of Differential Equation**

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

**Particular Solution of Differential Equation**

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

**Degree of Differential Equation**

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

**1 incorrect**

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

**False**

The equation y2= cx is general solution of:

**y’ = y / 2x**

Classify the following differential equation:

**Both separable and linear**

Determine the order and degree of the differentialequation:

**Fourth order, first degree**

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

**False**

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

**05 incorrect**

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

**False**

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

**True**

Which of the following equations is a variable separable DE?

**2ydx = (x2+ 1)dy**

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

**True**

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

**5sin4x + c**

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