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Differential-equations Questions Set 2:

Quiz Mode

Find ∂z/∂x where z = ax² + 2by² + 2bxy.

3by

2ax

3(ax+by)

2(ax+by)

Solution:

Differentiate tan^-1(√(1+x²) + 1/x)

-1/2(1+x)

1/2(1+x)

1/2(1+x²)

-1/2(1+x²)

Solution:

If f(x) = x⁹ e⁻ˣ, then the ninth derivative of f(x) at x = 0 is given by:

10!

21!

9! * e⁹

Solution:

Find ∂z/∂x where z=sin(x^2)×cos(y^2).

2x sin(x^2)

x sin(2x)

2x sin(x^2) cos(y^2)

6x sin(x^2) cos(y^2)

Solution:

Find the singular solution of the equation y = px + a/p.

y - 2ax = 0

y + 2ax = 0

y^2 + 4ax = 0

y^2 - 4ax = 0

Solution:

If the characteristic equation of the differential equation d²y/dx² + 2∝dy/dx + y = 0 has equal roots, then the value of ∝ is:

±1

±i

±1/2

0, 0

Solution:

The first and second derivatives of a quadratic polynomial at x = 1 are 1 and 2 respectively. Then the value of f(1) - f(0) is given by?

1.5

0.5

Solution:

Find the particular solution of the given differential equation (D² + 4D + 4)y = 0, given that y = 0 and y' = -1 at x = 1.

(1 - x)e^2(1-x)

(1 + x)e^2(1+x)

(1 - 2x)e^2(1-x)

(1 + 2x)e^2(1+x)

Solution:

Find the Complementary function for the given equation D³y + D²y + 4Dy + 4y = 0

c₁e^x + c₂cos(2x) + c₃sin(2x)

c₁e^x + c₂sin(2x) + c₃cos(2x)

c₁e^-x + c₂cos(2x) + c₃sin(2x)

c₁e^-x + c₂sin(2x) + c₃cos(2x)

Solution:

For the differential equation d²x/dt² + 6dx/dt + 8x = 0 with initial conditions x(0) = 1 and dx/dt = 0 at t = 0, the solution is:

x(t) = e^-2t + 2e^-4t

x(t) = 2e^-6t - e^-2t

x(t) = 2e^-2t - e^-4t

x(t) = -e^-6t + 2e^-4t

Differential-equations Questions Set 2:

Find ∂z/∂x where z = ax² + 2by² + 2bxy.

Solution:

Differentiate tan^-1(√(1+x²) + 1/x)

Solution:

If f(x) = x⁹ e⁻ˣ, then the ninth derivative of f(x) at x = 0 is given by:

Solution:

Find ∂z/∂x where z=sin(x^2)×cos(y^2).

Solution:

Find the singular solution of the equation y = px + a/p.

Solution:

If the characteristic equation of the differential equation d²y/dx² + 2∝dy/dx + y = 0 has equal roots, then the value of ∝ is:

Solution:

The first and second derivatives of a quadratic polynomial at x = 1 are 1 and 2 respectively. Then the value of f(1) - f(0) is given by?

Solution:

Find the particular solution of the given differential equation (D² + 4D + 4)y = 0, given that y = 0 and y' = -1 at x = 1.

Solution:

Find the Complementary function for the given equation D³y + D²y + 4Dy + 4y = 0

Solution:

For the differential equation d²x/dt² + 6dx/dt + 8x = 0 with initial conditions x(0) = 1 and dx/dt = 0 at t = 0, the solution is:

Solution:

Related Question Sets:

Related Topics:

Differential-equations Questions Set 2:

Find ∂z/∂x where z = ax² + 2by² + 2bxy.

Solution:

Differentiate tan-1(√(1+x²) + 1/x)

Solution:

If f(x) = x⁹ e⁻ˣ, then the ninth derivative of f(x) at x = 0 is given by:

Solution:

Find ∂z/∂x where z=sin(x^2)×cos(y^2).

Solution:

Find the singular solution of the equation y = px + a/p.

Solution:

If the characteristic equation of the differential equation d2y/dx2 + 2∝dy/dx + y = 0 has equal roots, then the value of ∝ is:

Solution:

The first and second derivatives of a quadratic polynomial at x = 1 are 1 and 2 respectively. Then the value of f(1) - f(0) is given by?

Solution:

Find the particular solution of the given differential equation (D2 + 4D + 4)y = 0, given that y = 0 and y' = -1 at x = 1.

Solution:

Find the Complementary function for the given equation D3y + D2y + 4Dy + 4y = 0

Solution:

For the differential equation d2x/dt2 + 6dx/dt + 8x = 0 with initial conditions x(0) = 1 and dx/dt = 0 at t = 0, the solution is:

Solution:

Related Question Sets:

Related Topics:

Differentiate tan^-1(√(1+x²) + 1/x)

If the characteristic equation of the differential equation d²y/dx² + 2∝dy/dx + y = 0 has equal roots, then the value of ∝ is:

Find the particular solution of the given differential equation (D² + 4D + 4)y = 0, given that y = 0 and y' = -1 at x = 1.

Find the Complementary function for the given equation D³y + D²y + 4Dy + 4y = 0

For the differential equation d²x/dt² + 6dx/dt + 8x = 0 with initial conditions x(0) = 1 and dx/dt = 0 at t = 0, the solution is: