Linear Differential Equations

Question	Answer
D'Alembert Formula	Image: Screen_Shot_2014-05-21_at_16.50.31 (image/png)
Power Series - Radius of Convergence	Image: Screen_Shot_2014-05-21_at_17.46.35 (image/png)
Method of Frobenius	Image: Screen_Shot_2014-05-21_at_18.04.23 (image/png)
Discrimant classification b^2 - ac <, = , >	>0 => PDE is Hyperbolic =0 => PDE is Parabolic
Image: Screen_Shot_2014-05-22_at_14.38.47 (image/png)	Image: Screen_Shot_2014-05-22_at_14.39.23 (image/png)
Reduction of order	If we know one solution of a 2nd homogenous equation, y(x) We look for a second solution of the for y = y(x)u(x) Note: u(x) will be simpler
Variation of Parameters y''+p1(x)y'+p0(x)y=q(x)	if we know y=Ay(x)+By(x) is a solution of the homogenous equation, then look solutions of the form y=A(x)y(x)+B(x)y(x) Differentiate and set A'y1 + B'y2 = 0 Find y' and y'' and sub. back into the original equation. Giving A'y1' + B'y2' = q(x) Solve for A(x), B(x)
2nd Order Linear Homogeneous ODE w. Constant coefficients y''+ay'+by=0	Image: Screen_Shot_2014-05-22_at_15.18.16 (image/png)
Legendre's Equation	Image: Screen_Shot_2014-05-22_at_15.42.25 (image/png)
Bessel's Equations	Image: Screen_Shot_2014-05-22_at_15.57.05 (image/png)
Laguerre's Equation	Image: Screen_Shot_2014-05-22_at_16.02.35 (image/png)
Hermite's Equation	Image: Screen_Shot_2014-05-22_at_16.06.19 (image/png)

Resource summary

	Created by joe_fresen over 11 years ago