Question 1

The equation $h(x)u(x) = f(x)+\int_a^b(x)K(x,\xi)u(\xi)d\xi ~ ext{for all}~ x\in[a,b]$ represents an integral equation.

Accepted Answer

true

Answer

false

Question 2

Observe the given equation:

Accepted Answer

Volterra integral equation of the second kind

Answer

It's a Volterra Integral equation

Answer

None of the above

Answer

Fredholm integral equation

Question 3

The conversion of given IVP $h(x)u(x) = f(x)+\int_a^b(x)K(x,\xi)u(\xi)d\xi ~ ext{for all}~ x\in[a,b]$ leads to

Accepted Answer

$y(x) =\frac{x^2}{2}-\int_0^x (x-\xi)*\xi *y(\xi) *d\xi$

Answer

$y(x) =\frac{x^2}{2}-\int_0^x (x-\xi)*\xi *y(\xi) *d\xi$

Answer

None of the above

Answer

$y(x) =\frac{x^2}{2}-\int_0^x (x-\xi)*\xi *y(\xi) *d\xi$

Question 4

What is the type of given integral equation: $h(x)u(x) = f(x)+\int_a^b(x)K(x,\xi)u(\xi)d\xi ~ ext{for all}~ x\in[a,b]$ .

Accepted Answer

None of the above

Answer

Homogeneous linear integral equation

Answer

Nonhomogenous nonlinear Fredholm integral equation

Answer

Linear Fredholm integral equation

Question 5

The Fredholm integral equation $h(x)u(x) = f(x)+\int_a^b(x)K(x,\xi)u(\xi)d\xi ~ ext{for all}~ x\in[a,b]$ is the outcome for the consideration of the following BVP $y''+2xy=1,~ 0 .$

Accepted Answer

true

Answer

false

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