Differential equation formulae
Power series :
Y=a0 +a1 x +a2 x2 +a3x3+………..
Y’ = a1 +2a2x+3a3x2+…………
Y’’=2a2+6a3x+………
Laplace transformation:
S-shifting theorem:
[f(t)]=f(s)
[ f(t)]=f(s-a)
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Differential Equations: Power Series and Laplace Transform, Summaries of Differential Equations
Formulas for solving differential equations using power series and laplace transformation. It includes the power series representation of a function and its derivative, the laplace transformation formula, and the convolution theorem. Useful for students in mathematics, engineering, and physics.
Typology: Summaries
2019/2020
1 / 2
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Differential equation formulae Power series : Y=a 0 +a 1 x +a 2 x 2 +a 3 x 3 +……….. Y ’ = a 1 +2a 2 x+3a 3 x 2 +………… Y ’’ =2a 2 +6a 3 x+……… Laplace transformation: S-shifting theorem: [f(t)]=f(s) [ f(t)]=f(s-a)
Laplace transform: General formulla [y n ]=s n [y]^ +s n- f(0)-s n- f ‘ (0)-……f n- (0). (fg)t= f(T) g(t-T)Dt* Z=e r/αx f(βx+αy) (αDx-ΒdY-r)z= (Since: r=gamma)