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 : ylog y dx - xdy = 0

a) Y = e
b) Y = e^x
c) Y = e^cx
d) None of these

✔Answer

Correct Answer Is : Y = e^cx

Solution Is :

Evaluate: cos(dy/dx) = a(a Є R); y = 1 when x = 0.

a) Cos(y - 1) = a
b) Cos(y - 1/x) = a
c) Cos(y + 1/x) = a
d) Cos(y + 1) = a

✔Answer

Correct Answer Is : Cos(y - 1/x) = a

Solution Is :

Find the equation of a curve passing through the point (0 , 0) and whose differential equation is y` = e^ sin x.

a) 2y - 1 = e^x (sin x - cos x)
b) 2y - 1 = e^x (sin x + cos x)
c) 2y - 1 = e^x
d) 2y + 1 = e^x (sin x - cos x)

✔Answer

Correct Answer Is : 2y - 1 = e^x (sin x - cos x)

Solution Is :

The slope of a tangent to the curve in the coordinate axis is given by the relation:

a) Xy
b) Dy/dx
c) Dy*dx
d) X/y

✔Answer

Correct Answer Is : Dy/dx

Solution Is :

Evaluate: y` = (x + y/x)

a) Y = xlog x
b) Y = xlog x + Cx
c) Y = log x + Cx
d) Y = x + Cx

✔Answer

Correct Answer Is : Y = xlog x + Cx

Solution Is :

True or false: the differential equation of the family of hyperbolas having foci on x-axis and centre at the origin xyy" + x(y`)^2 - yy` = 0.

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

✔Answer

Correct Answer Is : TRUE

Solution Is :

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 :

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Quantitative Aptitude Practice Calculus Study Material

Differential Equations

Evaluate : ylog y dx - xdy = 0

Correct Answer Is : Y = e^cx

Solution Is :

Evaluate: cos(dy/dx) = a(a Є R); y = 1 when x = 0.

Correct Answer Is : Cos(y - 1/x) = a

Solution Is :

Find the equation of a curve passing through the point (0 , 0) and whose differential equation is y` = e^ sin x.

Correct Answer Is : 2y - 1 = e^x (sin x - cos x)

Solution Is :

The slope of a tangent to the curve in the coordinate axis is given by the relation:

Correct Answer Is : Dy/dx

Solution Is :

Evaluate: y` = (x + y/x)

Correct Answer Is : Y = xlog x + Cx

Solution Is :

True or false: the differential equation of the family of hyperbolas having foci on x-axis and centre at the origin xyy" + x(y`)^2 - yy` = 0.

Correct Answer Is : TRUE

Solution Is :

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 :

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