Differential Equations - 17 - Mathematics MCQ

I₁ = - I₂

I₁ = I₂

I₁I₂ = -1

2xy sin xy

2xy cos xy

e^x

e^-x

log x

e^xy

e^x+ydx + sin x cos y dy = 0

sin (x + y)dx + cos (xy)dy = 0

(x + e^y)dx + (y - x)dy = 0

e^xy dx + sin (x + y)dy = 0

dy = (e^xy + x² e^-y) dx

tan y dy = [sin (x + y) + sin (x - y)]dx

All of the above equations are with separated variables

x + 2y - 1 = v    

x - y + 1 = v

x + y = v    

none of the above

2x + 3y = v

4x + 6y + 5 = v

3y + 2x + 4 = v

3x + 2y = v

(x² - y²)dx + 2xydy = 0

(1 + e^x/y)dx + e^x/y(1 - x/y)dy = 0

(2x - 3y - 5)dy + (3x + 2y - 5) dx = 0

A differential equation is exact if it is with separated variables

If a differential equation is exact, then it is with separated variables but not conversely

If a differential equation is with separated variables, then it is exact

If a differential equation is exact, then it is with separated variables

Circles

Parabolas

Ellipse

Straight lines passing through the origin

Parabolas

Hyperbolas

Circles

Ellipses

Can always be reduced to an exact form

Can never be reduced to an exact form

May or may not. be reduced to an exact form

Can only be reduced to an exact form if the given differential equation is linear

Can always be reduced to an equation with separated variables

Can never be reduced to an equation with separated variables

May or may not be reduced to an equation with separated variable

Can only be reduced to an equation with separated variables when the given equation is linear

y = v/x

y = vx

y = vx²

y = v/x²

x = X - 3, y = Y - 4

x = X + 1/3, y = Y + 4/3

x = X + 5, y = Y - 4

x = X - 5, y = Y + 4

2

0

-1

1

P(x) only

Q(x) only

both P(x) and Q(x)

P(x) but may or may not depend upon Q(x)