# Differential Equations - Online Test

Q1. Differential equations are equations containing functions y = f(x), g(x) and
Explaination / Solution:

Differential equations are equations containing functions y = f(x), g(x) and derivatives of y with respect to x.

Q2. Order of a differential equation is defined as
Explaination / Solution:

Order of a differential equation is defined as the order of the highest order derivative of the dependent variable present in the differential equation.

Q3. Degree of a differential equation, when the equation is polynomial equation in y′ is
Explaination / Solution:

The power or index of the highest ordered derivative in the polynomial is the degree of the differential equation provided equation is in the standard form.

Q4. The order of the equation  is
Explaination / Solution:

Since the equation has 2nd derivative as the highest derivative term.hence the order 2

Q5. The order of the equation = 0 is
Explaination / Solution:

Since the highest derivative term is  hence the order is 3.

Q6. The degree of the equationis
Explaination / Solution:

the power of the highest order derivative i.e . is 2.hence the degree 2

Q7. Find the order and degree of is
Explaination / Solution:

Order = 3 ,Since the highest order derivative is  but degree cannot be defined ,because the deriative term  y’ is present in exponential form.
Q8. Determine order and degree (if defined) of +sin(y’’’) = 0
Explaination / Solution:

Order = 4 , degree not defined , because the function y’’’ present in the angle of sine function.

Q9. Determine order and degree (if defined) of y’ + 5y = 0
Explaination / Solution:

Order = 1 , degree = 1. Since the equation has the highest derivative as y' and its power is 1

Q10. Determine order and degree (if defined) of  + 3s = 0
Explaination / Solution:

Order = 2 , degree = 1.Since the equation has  as the highest derivative term.its order is 2 and its index is 1