When solving a variables separable ODE such as:

dy/dx=f(x) => intergral dy = integral f(x) dx

what limits does one integrate between??????

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- Apr 7th 2008, 05:11 AMjohnbarkwithvariables separable ODE
When solving a variables separable ODE such as:

dy/dx=f(x) => intergral dy = integral f(x) dx

what limits does one integrate between?????? - Apr 7th 2008, 06:13 AMmr fantastic
If the boundary condition is given, then

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If the boundary condition is given and the the value of y when is required, then

.

Otherwise there are no limits:

and the right hand side is an indefinite integral. Of course, this approach can also be taken when boundary conditions*are*given - see the next reply. - Apr 7th 2008, 06:13 AMawkward
Usually you don't use limits on the integral. You evaluate the indefinite integral and add in a constant of integration. Then if you have an initial value for your differential equation you use it to find the value of the constant.

- Apr 7th 2008, 10:41 AMMathstud28Maybe
this sample example will help ...seperating we get then by integrating we get multiplying both sides by we get and using the rules of ratios we can switch the means to give us finally by taking the cuberoot of each side we arrive at our answer