Question

what is the difference b\w initial value and boundry value problems ?in differential equations .

Answer 1

nothing really just a fancy name

Answer 2

an initial value problem is when all your conditions are initial conditions , ie when time =0.

So say the equation was modelling temperate (T)

we might have conditions when t=0 , dT/dt = -1 and T = 20

Answer 3

a boundary value problem is when your conditions are not at t=0 ( or when you have one of the conditions that is not an initial condition )

so back to the temperature example , we might have conditions when t=0 , dT/dt + +2 , and when t= 3 , dT/dt =-1

Answer 4

where our conditions are not at the starting point ( or atleast one of them isnt )

Answer 5

nevertheless, they are still solved the exact same way

Say I took an easy example , dy/dx = x^2 , and when x=0, y= 1

we would get y= (1/3)x^3 +C , and you would sub in the condition to find C=1

Now if I had the "boundary value " problem dy/dx=x^2 , y=3 when x= 2

we would get y= (1/3)x^3 +C , and we would sub in the condition to find the C