Karteikarten
ODE's
Karten in diesem Stapel (10)
- 1Variable Separable Method1. Separate the variables (get all the x and all the y on separate sides)
2. Integrate, then rearrange to obtain the general solution 'y = ...'
3. Use the given condition to find the particular solution - 2Integration factorα(x) = exp Z
p(x)dx - 3Integration factor method1. Find the integration factor
Multiply both sides of the differential equation by the integration factor
2. Use the product rule to re-write the left hand side
3. Integrate both sides with respect to x, then rearrange to obtain the general solution
4. Use the given condition to obtain the particular solution - 4Homogeneous Equations - Distinct Real Roots(b2 > 4ac)
GENERAL SOLUTION: y = Aem1x + Bem2x - 5Homogeneous Equations - Complex Rootsb2 < 4ac
The solution to the auxiliary equation will be m = α ± βi - 6Homogeneous Equations - Repeated (real) rootsb2 = 4ac
GENERAL SOLUTION: y = (A + Bx)emx - 7Homogeneous Equations1. Identify the auxiliary equation
2. Obtain the values of m
3. determine if the solution is real, complex or distinct and construct the general solution
4. Use the given conditions to obtain the particular solution - 8Inhomogeneous equation - complimentary solutionThe complementary solution, yC, the general solution to the equivalent homogeneous equation
- 9Inhomogeneous equation - particular integralThe particular integral, yI , a specifically chosen function, selected such that when it is substituted into the inhomogeneous equation it yields the function f(x)
- 10Inhomogeneous equations1. find the complimentary solution (yc)
2. Select an appropriate particular integral (yi)
3. substitute the particular integral into the equation
4. combine the complimentary function and particular integral to obtain the general solution
5. Use the given conditions to obtain the particular solution
Informationen
- Beschreibung
- Degree level Further Mathematics for Engineers (Ordinary Differential Equations) Karteikarten am ODE's, erstellt von rhiannonsian am 09/04/2015.
- Erstellt von
- rhiannonsian
- Aufrufe
- 2
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