Differential equations are equations containing functions y = f(x), g(x) and

**A. ** minima of y

**B. ** maxima of y

**C. ** derivatives of y

**D. ** tangent of y at zero

**Answer : ****Option C**

**Explaination / Solution: **

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

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

Workspace

Report

The degree of the equationis

**A. ** 1

**B. ** 2

**C. ** 0

**D. ** 3

**Answer : ****Option B**

**Explaination / Solution: **

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

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

Workspace

Report

Determine order and degree (if defined) ofcos() = 0

**A. ** 0,degree undefined

**B. ** 2,degree undefined

**C. ** 3,1

**D. ** 1,degree undefined

**Answer : ****Option B**

**Explaination / Solution: **

order = 2, degree not defined, because the function dy/dx present in angle of cosine function.

order = 2, degree not defined, because the function dy/dx present in angle of cosine function.

Workspace

Report

General solution of a given differential equation

**A. ** contains exactly one arbitrary constant

**B. ** contains exactly two arbitrary constants

**C. ** contains arbitrary constants depending on the order of the differential equation

**D. ** does not contain arbitrary constants

**Answer : ****Option C**

**Explaination / Solution: **

The general solution of differential equation contains arbitrary constants equal to the order of differential equaition.

The general solution of differential equation contains arbitrary constants equal to the order of differential equaition.

Workspace

Report

General solution of is

**A. ** y = 1 + Ae−3x
**B. ** y = 1 + Aex
**C. ** y = 1 + Ae-x
**D. ** y = B + Ae−x
**Answer : ****Option C**

**Explaination / Solution: **

It is of the form of linear differential equation.hence the solution is y X IF =

Workspace

Report

General solution of
**A. ** tanx2=C(1−ex)
**B. ** tany2=C(1−ex)
**C. ** tany3=C(1−ex)

**D. ** tany

=C(1−ex)

**Answer : ****Option D**

**Explaination / Solution: **

=C(1−ex)

Workspace

Report

Find the particular solution of the differential equation , given that y = 0 and x = 0.

**A. ** 4e3x+3e−4y+7=0
**B. ** 4e3x−3e−4y−7=0
**C. ** 4e3x+3e−4y−7=1
**D. ** 4e3x+3e−4y−7=0

**Answer : ****Option D**

**Explaination / Solution: **

Workspace

Report

To form a differential equation from a given function

**A. ** Differentiate the function successively as many times as the number of arbitrary constants inthe given function and eliminate the arbitrary constants.

**B. ** Differentiate the function once and eliminate the arbitrary constants

**C. ** Differentiate the function once and add values to arbitrary constants

**D. ** Differentiate the function twice and eliminate the arbitrary constants

**Answer : ****Option A**

**Explaination / Solution: **

We shall differentiate the function equal to the number of arbitrary constant so that we get equations equal to arbitrary constant and then eliminate them to form a differential equation

We shall differentiate the function equal to the number of arbitrary constant so that we get equations equal to arbitrary constant and then eliminate them to form a differential equation

Workspace

Report

Forming a differential equation representing the given family of curves by eliminating arbitrary constants a and b from y = (a cosx + b sinx) yields the differential equation

**A. ** y″ + 2y′ - 2y = 0

**B. ** y″ – 2y′ - 2y = 0

**C. ** y″ +2y′ + 2y = 0

**D. ** y″ – 2y′ + 2y = 0

**Answer : ****Option D**

**Explaination / Solution: **

Workspace

Report

Find the equation of a curve passing through the point (0, –2) given that at any point (x, y) on the curve, the product of the slope of its tangent and y coordinate of the point is equal to the x coordinate of the point.

**A. ** y3− x2= 4
**B. ** y2− x2= 4
**C. ** y3− x3= 4
**D. ** y2− x3= 4
**Answer : ****Option B**

**Explaination / Solution: **

Workspace

Report