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Differential Equations and Solutions
Question 1
What is a differential equation?
An equation involving only algebraic terms
An equation involving derivatives of a function
An equation with no variables
An equation that has only constants
Question 2
Which of the following is an ordinary differential equation?
y = mx + b
[Tex]\frac{d^2 y}{dx^2} + 3 \frac{dy}{dx} + 2y = 0[/Tex]
x2+y2=r2
[Tex]a^2 + b^2 = c^2
[/Tex]
Question 3
Solve the differential equation dy/dx=2x.
y = 2x + C
y = x2 + C
y = 2x2 + C
y = x + C
Question 4
A population of bacteria doubles every hour. If the initial population is P0, which differential equation models the population growth?
dP/dt = P0
dP/dt = 2P
dP/dt = P
dP/dt = P/2
Question 5
If y= e2x is a solution to a differential equation, which of the following could be the differential equation?
dy/dx=y
dy/dx=2y
dy/dx=y/2
dy/dx=−2y
Question 6
The order and degree of the differential equation
[Tex]{\left( {1 + 3{{dy} \over {dx}}} \right)^{2/3}} = 4{{{d^3}y} \over {d{x^3}}}[/Tex] are
[Tex]\left( {1,{2 \over 3}} \right)[/Tex]
[Tex](3, 1)[/Tex]
[Tex](3,3)[/Tex]
[Tex](1,2)[/Tex]
Question 7
The order of the differential equation whose solution is[Tex] y=a \cos x+b \sin x+c e^{-x}[/Tex] is
3
4
2
1
Question 8
By eliminating the arbitrary constants from[Tex] y=(a+b) \sin (x+c)-d e^{x+e+f}[/Tex] then differential equation has order of
6
4
3
5
Question 9
The order of the differential equation of all parabolas whose axis of symmetry along X-axis is
2
3
1
None of these
Question 10
The differential equation representing the family of curves [Tex]{y^2} = 2c\left( {x + \sqrt c } \right)[/Tex] where [Tex]c>0,[/Tex] is a parameter, is of order and degree as follows:
order [Tex]1,[/Tex] degree [Tex]2[/Tex]
order [Tex]1,[/Tex] degree [Tex]1[/Tex]
order [Tex]1,[/Tex] degree [Tex]3[/Tex]
order [Tex]2,[/Tex] degree [Tex]2[/Tex]
There are 10 questions to complete.