Final Exam Review - Solution Requirements Flashcards
What type of solution do you get, and what are the requirements for integrating factor?
General solution, and first order non/homogeneous DE in standard form dy/dx+P(x)y=f(x0
What type of solution do you get, and what are the requirements for exact equations and special notes?
General solution, and first order homogeneous DE in standard form M(x,y) dx + N(x,y) dy where pM/py = pN/px
What type of solution do you get, and what are the requirements for substitution and special notes?
General solution, and first order homogeneous DE with M(x,y) and N(x,y) of the same degree, pM/pY =/= pN/px. Choose the ‘simpler’ variable to perform the substitution.
What type of solution do you get, and what are the requirements for Bernoulli substitution and special notes?
General solution, and first order nonhomogeneous DE in dy/dx + P(x)y = y^n * g(x) form. Aiming for integrating factor form.
Where can second solution be used?
Second order differential equations of any homogeneity where the first solution has already been provided
What type of solution do you get, and what are the requirements for Auxiliary Equation and special notes?
General or yc for NH, and both NH and H equations of any order. Requires constant coefficients.
What type of solution do you get, and what are the requirements for Method of Undetermined Coefficients and special notes?
yp, and nonhomogeneous equations of any order. Requires constant coefficients and g(x) must have an annihilator.
What type of solution do you get, and what are the requirements for Variation of Parameters and special notes?
yp, and nonhomogeneous second order or higher DEs. Requires variable coefficients and g(x) containing functions with no annihilator.
What type of solution do you get, and what are the requirements for Cauchy-Euler and special notes?
General or yc for NH, and both NH and H equations of 2nd order or higher. Requires variable coefficients, equation must be in a(x-x0)^2d^2y/dx^2+b(x-x0)dy/dx+cy=0 form
What type of solution do you get, and what are the requirements for Systems - Elimination and special notes?
General/Yc for NH, and both NH and H first order DEs. Requires systems with constant coefficients.
What type of solution do you get, and what are the requirements for Power Series and special notes?
General, and H DEs of 2 order maximum. Coefficient on derivative must be nonsingular (not equal to 0 or infinity)
What type of solution do you get, and what are the requirements for Infinite Series and special notes?
General, and H DEs of 2 order maximum. Use a second solution if only one solution is found.
What type of solution do you get, and what are the requirements for Laplace Transform and special notes?
General, and H and NH DEs of any order. Requires constant coefficients.
What type of solution do you get, and what are the requirements for Systems - Eigenvalues and special notes?
General, and H DEs of first order. Requires constant coefficients.
