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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.

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

**Integrating factor**

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

**General Solution of Differential Equation**

Integration is the reverse process of differentiation

**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 bydy/dx+4y=sinx?

**05 incorrect**

The differential equationis

**Linear**

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**

The equation y2= cx is general solution of:

**y’ = y / 2x**

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

**Particular Solution of Differential Equation**

For the differential equation dy/dx = 4sin2x, what is the particular solution if y=2 when x=pi/2

**-2cos2x**

is a second order ordinary differential equation

**False**

is a first orderpartial differential equation

**True**

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

**True**

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

**True**

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

**3 incorrect**

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

**Differential Equations**

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

**y=3+c/x**

The general solution of the differential equation 2x(dy/dx)=3-x3is

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

Determine the order and degree of the differentialequation:

**Fourth order, first degree**

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

**True**

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

**False**

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

**True**

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

**False**

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

**False**

Which of the following equations is a variable separable DE?

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

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

**False**

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

**True**

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

**False**

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

**True**

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

**Acos2t + Bsin2t**

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

**lny=2sinx+c**

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

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

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

**Degree of Differential Equation**

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

**5sin4x + c**

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

**All of the above**

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

**True**

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

**True**

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

**1 incorrect**

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

**Partial Differential Equation**

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

**True**

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

**-4cos2x+c**

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

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

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

**Linear**

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

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

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

**xy2+y3=c**

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

**4 incorrect**

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