Solving Differential Equations
any IVP
Yes: insert IVP into general solution
No: find general solution
General Solution
Higher Order DE
Homogenous?
Yes: Find Homogenous Solution
Use Complex Characteristic Roots
Use Real Charaacteristic Roots
Check for repeated roots
Use Undetermined Coefficients
Use Variation of Parameter
No:Find Homogenous and Particular Solution y(t) = yh(t) + yp(t) (Non-homogenous)
Laplace Transformation
System of first order DE
Use Eigenvalues and Eigenvectors
Any of the other used to find Homogenous solution
First Order DE
Integrate Directly?
Yes: Integrate and solve for y
No: try and separate
Separtable?
Yes: integrate and solve for y
No: Try integrating Factor
Can be written in the form y'+P(t)=f(t)
Yes: use integrating Factor
No:Use Euler's Method