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Differential-equations Questions Set 1:

Quiz Mode

Let f(x) = ln(1 - x)e^x. Find the third derivative of f(x) at x = 0.

1/3

Undefined

0.25

Solution:

Find ∂z/∂y of the given equation:

z = 8xy + 12x²y - 9y² + 2x²

4x(2x + 3) - 18y

8y(1 + 3x) + 4x

8y(3 + x) + 4x

4x(2 + 3x) - 18y

Solution:

The value of y at t=5 for the given differential equation is dy/dt = - 6y; initial condition y = 3 at t=0

6e^-15

3e^-30

6e^-30

3e^-15

Solution:

Obtain the Z-transform of the following sequence:

U_n = (n+1)²

(z^2 + z)/(z-1)^2

(z^2 + z^3)/(z-1)^2

(z + z^3)/(z-1)^3

(z^2 + z^3)/(z-1)^3

Solution:

Find the partial derivative of z with respect to x for the given equation:

z = 5x²y + 3xy - 2y

y (5x + 3)

x (5y + 3)

x (5xy + 3) - 2y

y (10x + 3)

Solution:

What is the general solution of the equation: d²y/dx² - 5dy/dx + 6y = 0?

none of the above

c1*e^x + c2*e^(2x)

c1*e^(2x) + c2*e^(3x)

c1*(e^(2x) + e^(3x))

Solution:

The solution of y⁵x + y - x dy/dx = 0 is

( y^5/5 ) + ( y^4/4 x^4 ) = c

( x^5/5 y^5 ) + ( x^4/4 ) = c

( y^5/5 x^5 ) + ( y^4/4 ) = c

( x^5/5 ) + ( x^4/4 y^4) = c

Solution:

The ends X and Y of a rod of 30 cm length are kept at 40°C and 100°C until steady state prevails. What is the temperature function u(x,0)?

60 + 2x

40 + 2x

2 + 40x

2 + 60x

Solution:

The p-th derivative of a q-th degree monic polynomial, where p and q are positive integers and 2p⁴ + 3pq³⁄₂ = 3q³⁄₂ + 2qp³, is given by?

Cannot be generally determined

(q - 1)!

(q - 1)! * pq

Solution:

Find the general solution of the differential equation yp² + (x-y)p - x = 0

(y + x - c)(y^2 + x^2 - c1) = 0

(y - x - c)(y^2 + x^2 - c1) = 0

(1 - x/y - c)(y^2 - x^2 - c1) = 0

(1 + x/y -c)(y^2 + x^2 -c1) = 0

Differential-equations Questions Set 1:

Let f(x) = ln(1 - x)e^x. Find the third derivative of f(x) at x = 0.

Solution:

Find ∂z/∂y of the given equation:

z = 8xy + 12x²y - 9y² + 2x²

Solution:

The value of y at t=5 for the given differential equation is dy/dt = - 6y; initial condition y = 3 at t=0

Solution:

Obtain the Z-transform of the following sequence:

U_n = (n+1)²

Solution:

Find the partial derivative of z with respect to x for the given equation:

z = 5x²y + 3xy - 2y

Solution:

What is the general solution of the equation: d²y/dx² - 5dy/dx + 6y = 0?

Solution:

The solution of y⁵x + y - x dy/dx = 0 is

Solution:

The ends X and Y of a rod of 30 cm length are kept at 40°C and 100°C until steady state prevails. What is the temperature function u(x,0)?

Solution:

The p-th derivative of a q-th degree monic polynomial, where p and q are positive integers and 2p⁴ + 3pq³⁄₂ = 3q³⁄₂ + 2qp³, is given by?

Solution:

Find the general solution of the differential equation yp² + (x-y)p - x = 0

Solution:

Related Question Sets:

Related Topics:

Differential-equations Questions Set 1:

Let f(x) = ln(1 - x)e^x. Find the third derivative of f(x) at x = 0.

Solution:

Find ∂z/∂y of the given equation: z = 8xy + 12x²y - 9y² + 2x²

Solution:

The value of y at t=5 for the given differential equation is dy/dt = - 6y; initial condition y = 3 at t=0

Solution:

Obtain the Z-transform of the following sequence: Un = (n+1)2

Solution:

Find the partial derivative of z with respect to x for the given equation: z = 5x²y + 3xy - 2y

Solution:

What is the general solution of the equation: d2y/dx2 - 5dy/dx + 6y = 0?

Solution:

The solution of y5x + y - x dy/dx = 0 is

Solution:

The ends X and Y of a rod of 30 cm length are kept at 40°C and 100°C until steady state prevails. What is the temperature function u(x,0)?

Solution:

The p-th derivative of a q-th degree monic polynomial, where p and q are positive integers and 2p⁴ + 3pq³⁄₂ = 3q³⁄₂ + 2qp³, is given by?

Solution:

Find the general solution of the differential equation yp2 + (x-y)p - x = 0

Solution:

Related Question Sets:

Related Topics:

Find ∂z/∂y of the given equation:

z = 8xy + 12x²y - 9y² + 2x²

Obtain the Z-transform of the following sequence:

U_n = (n+1)²

Find the partial derivative of z with respect to x for the given equation:

z = 5x²y + 3xy - 2y

What is the general solution of the equation: d²y/dx² - 5dy/dx + 6y = 0?

The solution of y⁵x + y - x dy/dx = 0 is

Find the general solution of the differential equation yp² + (x-y)p - x = 0