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A differential equation is basically an equations with derivatives in them, and to solve a differential equation is to find a function or functions that satisfies the equation.
The following pages are mostly part of the current IB Maths HL course.
- Differential equations – an introduction
- A few examples from the kinematics
- Separable differential equations
- Separable differential equations – A few illustrating examples
- To find particular solutions
- Homogenous functions
- Homogenous differential equations – a first type
- Linear differential equations
- First order linear differential equations
- First order linear differential equations – a couple of examples
- Using Taylor series to solve differential equations
- Simple harmonic motion again – using Taylor series
- Euler’s step method
- Simple harmonic motion –Euler’s step method
The following are not directly part of the IB Maths HL course.
- The Earth orbit and Euler’s Step method
- The order of operations
- Homogeneous differential equations – a more general type
- A harder example of solving a linear first order equation
A larger example – the Brine mixture problem
- Brine mixture, case 1, inflow=outflow, pure water in
- Brine mixture, case 2, inflow≠outflow, pure water in
- The limit of case 2
- Brine mixture, case 3, inflow=outflow, brine in
- Brine mixture, case 4, inflow≠outflow, brine in
- Solving the mixture problem using Euler’s step method
- Graphing all solutions – An interactive page.
The following pages are not part of the IB Maths HL course.
- Linear second-order equations with constant coefficients
- LSO -Two different real roots
- LSO – Two equal real roots
- LSO – Two complex roots
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