ENGR 213 Lecture 10: formulas_2

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2 Feb 2016
Department
Course
Professor
Formulas
First-order equations
y0+P(x)y=f(x)y=eRP(x)dxZf(x)eRP(x)dxdx
Second-order linear DE with constant coefficients
m=α±βi y=eαx (c1cos βx +c2sin βx)
m=m1(real double root) y= (c1+c2x)em1x
m=m1, m =m2(distinct real roots) y=c1em1x+c2em2x
Homogeneous second-order DE
y00 +P(x)y0+Q(x)y= 0
y2=y1Z1
y2
1
eRP(x)dxdx
Inhomogeneous second-order DE
y00 +P(x)y0+Q(x)y=f(x)
yp=u1(x)y1+u2(x)y2(u0
1=f(x)y2
y1y0
2y0
1y2
u0
2=f(x)y1
y1y0
2y0
1y2
Miscellaneous
For
X
n=0
cnxn, L = lim
n→∞
cn+1xn+1
cnxn
e= cos θ+isin θ
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