Thread: initial value problem

Given that y''=y'+2y and that y(0)=0 and y(1)=1 Deduce that one of the initial value problems has a trivial solution.

Please tell me how can I get the trivial answer. If we set y(0)=0 and y'(0)=0 we get the correct answer, but the answer is saying that y(0)=0 and y'(0)=1 is also trivial(!) which doesn't make sense to me.

An IVP, if I am not mistaken, refers to an equation together with a SINGLE value. What you have there looks more like a boundary problem. In any case, it has two values, so it's not an IVP.

Perhaps they mean to give you two IVPs with the same equation... ? In that case y(0)=0 is obviously the one with the trivial solution.

Originally Posted by immortality

Given that y''=y'+2y and that y(0)=0 and y(1)=1 Deduce that one of the initial value problems has a trivial solution.

Please tell me how can I get the trivial answer. If we set y(0)=0 and y'(0)=0 we get the correct answer, but the answer is saying that y(0)=0 and y'(0)=1 is also trivial(!) which doesn't make sense to me.

Originally Posted by immortality

Given that y''=y'+2y and that y(0)=0 and y(1)=1 Deduce that one of the initial value problems has a trivial solution.

You are given a boundary value problem. I don't know what "one of the initial value problems" means. One of what initial value problems? Certainly one possible initial value problem for this differential equation is "y''= y'+ 2y with y(0)= 0, y'(0)= 0". That uses the same equation and one of the given boundary values so perhaps that is what is meant.

Please tell me how can I get the trivial answer. If we set y(0)=0 and y'(0)=0 we get the correct answer, but the answer is saying that y(0)=0 and y'(0)=1 is also trivial(!) which doesn't make sense to me.

Originally Posted by hatsoff

An IVP, if I am not mistaken, refers to an equation together with a SINGLE value. What you have there looks more like a boundary problem. In any case, it has two values, so it's not an IVP.

An "initial value problem" for a second order equation would give a value of y and its derivative at a single value of the independent variable.

Perhaps they mean to give you two IVPs with the same equation... ? In that case y(0)=0 is obviously the one with the trivial solution.