Kategorier: Alle - equations - laplace

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Math2250

Math2250

Solving Differential Equations

First Order DE

Integrate Directly?
No: try and separate

Separtable?

No: Try integrating Factor

Can be written in the form y'+P(t)=f(t)

No:Use Euler's Method

Yes: use integrating Factor

Yes: integrate and solve for y

Yes: Integrate and solve for y

Higher Order DE

Homogenous?
No:Find Homogenous and Particular Solution y(t) = yh(t) + yp(t) (Non-homogenous)

Any of the other used to find Homogenous solution

System of first order DE

Use Eigenvalues and Eigenvectors

Laplace Transformation

Yes: Find Homogenous Solution

Use Variation of Parameter

Use Undetermined Coefficients

Use Real Charaacteristic Roots

Check for repeated roots

Use Complex Characteristic Roots

General Solution

any IVP

No: find general solution
Yes: insert IVP into general solution