what is the difference b\w initial value and boundry value problems ?in differential equations .
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nothing really just a fancy name
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
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
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where our conditions are not at the starting point ( or atleast one of them isnt )
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