Differential Equations help Watch

ollz272
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I'm alright with this question until i) 3), i'm confused about what it means by 'y is bounded by all x', and how it helps us get the arbitrary constants
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davros
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(Original post by ollz272)
I'm alright with this question until i) 3), i'm confused about what it means by 'y is bounded by all x', and how it helps us get the arbitrary constants
"y is bounded for all x" basically means that y can't become infinite anywhere - so for example if you had something like

y = (A/(x-2)) + Bx

then A would have to be 0 otherwise y wouldn't remain bounded as x got close to 2.

It's possible they also mean that y must remain finite as the independent variable gets very large - which rules out things like positive exponentials etc

These conditions help you eliminate some of the constants you get from a general solution to the DEs.
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ollz272
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(Original post by davros)
"y is bounded for all x" basically means that y can't become infinite anywhere - so for example if you had something like

y = (A/(x-2)) + Bx

then A would have to be 0 otherwise y wouldn't remain bounded as x got close to 2.

It's possible they also mean that y must remain finite as the independent variable gets very large - which rules out things like positive exponentials etc

These conditions help you eliminate some of the constants you get from a general solution to the DEs.
I have general solutions of y=Acos(3x)+Bsin(3x), and y=Ce^-4x + De^4x, where do i go from here? i know that cos and sin will be bounded by x forever since they oscillate between 2 values, but what about my exponential?
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davros
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(Original post by ollz272)
I have general solutions of y=Acos(3x)+Bsin(3x), and y=Ce^-4x + De^4x, where do i go from here? i know that cos and sin will be bounded by x forever since they oscillate between 2 values, but what about my exponential?
Are there any restrictions on x e.g. x > 0 or x < 0? De^4x is unbounded as x goes to infinity so if x has to be positive then D must be 0 for example.
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