Learn Calculus Differential Equations, Quantitative Aptitude Practice Calculus Differential Equations Exercise, Free Online Differential Equations Lessons

Quantitative Aptitude Practice Calculus Study Material

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Differential Equations

Evaluate: (x^2 - y^2)dx + 2xy dy = 0

a) (x^2 - y^2) = cx
b) (x^2 + y^2) = cx
c) (x + y) = cx
d) (x - y) = cx

✔Answer

Correct Answer Is : (x^2 + y^2) = cx

Solution Is :

Determine the order of the equation y` + 5y = 0.

a) 0
b) 1
c) 2
d) 3

✔Answer

Correct Answer Is : 1

Solution Is :

Determine the order of the equation (d^2y/dx^2)^2 + cos (dy/dx) = 0.

a) 0
b) 1
c) 2
d) 3

✔Answer

Correct Answer Is : 2

Solution Is :

Determine the order of the equation y` + y = e^x.

a) 0
b) 1
c) 2
d) 3

✔Answer

Correct Answer Is : 1

Solution Is :

True or false: y = e^x + 1: y" - y` = 0

a) TRUE
b) FALSE
c) Maybe
d) None of these

✔Answer

Correct Answer Is : TRUE

Solution Is :

The number of constants in general solution of a differential equation of order n is equal to its ____________ .

a) Order
b) Degree
c) Difference of order and degree
d) None of these

✔Answer

Correct Answer Is : Order

Solution Is :

The numbers of arbitrary constants in general solution of a differential equation of fourth order is?

a) 1
b) 2
c) 3
d) 4

✔Answer

Correct Answer Is : 4

Solution Is :

The equation of parabola having the vertex at origin and the axis along the positive y-axis is:

a) X^2 = 4ay
b) X^2 = 4ay^2
c) Y^2 = 4ax
d) Y^2 = 4ax^2

✔Answer

Correct Answer Is : X^2 = 4ay

Solution Is :

True or false:the differential equation has y=x as one of its partial solution (d^2y/dx^2 -x^2 dy/dx + xy =x).

a) TRUE
b) FALSE
c) Maybe
d) None of these

✔Answer

Correct Answer Is : FALSE

Solution Is :

Evaluate : dy/dx = (1 - cos x)/(1 + cos x)

a) Y = 2tan (x/2)
b) Y = 2tan (x/2) - x
c) Y = 2tan (x/2) + x
d) Y = 2tan (x/2) - x + c

✔Answer

Correct Answer Is : Y = 2tan (x/2) - x + c

Solution Is :

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Quantitative Aptitude Practice Calculus Study Material

Differential Equations

Evaluate: (x^2 - y^2)dx + 2xy dy = 0

Correct Answer Is : (x^2 + y^2) = cx

Solution Is :

Determine the order of the equation y` + 5y = 0.

Correct Answer Is : 1

Solution Is :

Determine the order of the equation (d^2y/dx^2)^2 + cos (dy/dx) = 0.

Correct Answer Is : 2

Solution Is :

Determine the order of the equation y` + y = e^x.

Correct Answer Is : 1

Solution Is :

True or false: y = e^x + 1: y" - y` = 0

Correct Answer Is : TRUE

Solution Is :

The number of constants in general solution of a differential equation of order n is equal to its ____________ .

Correct Answer Is : Order

Solution Is :

The numbers of arbitrary constants in general solution of a differential equation of fourth order is?

Correct Answer Is : 4

Solution Is :

The equation of parabola having the vertex at origin and the axis along the positive y-axis is:

Correct Answer Is : X^2 = 4ay

Solution Is :

True or false:the differential equation has y=x as one of its partial solution (d^2y/dx^2 -x^2 dy/dx + xy =x).

Correct Answer Is : FALSE

Solution Is :

Evaluate : dy/dx = (1 - cos x)/(1 + cos x)

Correct Answer Is : Y = 2tan (x/2) - x + c

Solution Is :

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