Definite Integration and Initial Value Problems
This video introduces a way to solve simple ODEs in the form $y' = f(x)$ simultaneously with an initial value problem, using definite integration. My differential equations book presents what appears to be a similar, definite integration in the section on separable differential equations, but in my opinion doesn't explain the step clearly enough to be helpful.
In the simplest terms possible, why is this algorithm equivalent to solving an initial value problem the traditional way, and how, if at all, can it be applied to ODEs that require more than simple integration (and perhaps more than separation of variables) and/or multiple "initial" values (i.e., problems with both a proportionality constant and an integration constant) to solve?
integration differential-equations definite-integrals indefinite-integrals initial-value-problems
asked Nov 25 at 21:07
user10478
388111
add a comment |
This video introduces a way to solve simple ODEs in the form $y' = f(x)$ simultaneously with an initial value problem, using definite integration. My differential equations book presents what appears to be a similar, definite integration in the section on separable differential equations, but in my opinion doesn't explain the step clearly enough to be helpful.
In the simplest terms possible, why is this algorithm equivalent to solving an initial value problem the traditional way, and how, if at all, can it be applied to ODEs that require more than simple integration (and perhaps more than separation of variables) and/or multiple "initial" values (i.e., problems with both a proportionality constant and an integration constant) to solve?
integration differential-equations definite-integrals indefinite-integrals initial-value-problems
asked Nov 25 at 21:07
user10478
388111
add a comment |
This video introduces a way to solve simple ODEs in the form $y' = f(x)$ simultaneously with an initial value problem, using definite integration. My differential equations book presents what appears to be a similar, definite integration in the section on separable differential equations, but in my opinion doesn't explain the step clearly enough to be helpful.
In the simplest terms possible, why is this algorithm equivalent to solving an initial value problem the traditional way, and how, if at all, can it be applied to ODEs that require more than simple integration (and perhaps more than separation of variables) and/or multiple "initial" values (i.e., problems with both a proportionality constant and an integration constant) to solve?
integration differential-equations definite-integrals indefinite-integrals initial-value-problems
asked Nov 25 at 21:07
user10478
388111
This video introduces a way to solve simple ODEs in the form $y' = f(x)$ simultaneously with an initial value problem, using definite integration. My differential equations book presents what appears to be a similar, definite integration in the section on separable differential equations, but in my opinion doesn't explain the step clearly enough to be helpful.
In the simplest terms possible, why is this algorithm equivalent to solving an initial value problem the traditional way, and how, if at all, can it be applied to ODEs that require more than simple integration (and perhaps more than separation of variables) and/or multiple "initial" values (i.e., problems with both a proportionality constant and an integration constant) to solve?
integration differential-equations definite-integrals indefinite-integrals initial-value-problems
integration differential-equations definite-integrals indefinite-integrals initial-value-problems
asked Nov 25 at 21:07
user10478
388111
asked Nov 25 at 21:07
user10478
388111
edited Nov 26 at 23:23
asked Nov 25 at 21:07
user10478
388111
asked Nov 25 at 21:07
user10478
388111
asked Nov 25 at 21:07
user10478
388111
388111
add a comment |
add a comment |
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